%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.33",
%%% date = "13 March 2019",
%%% time = "06:21:15 MST",
%%% filename = "kepler.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "http://www.math.utah.edu/~beebe",
%%% checksum = "14113 7693 32167 329963",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "Archimedean solid packing; BibTeX;
%%% bibliography; David Hilbert's 18th Problem
%%% (1900); Johannes Kepler (1571--1630); Kepler
%%% Conjecture; Kepler optimal sphere-packing
%%% problem; Kepler Theorem; kissing numbers;
%%% Platonic solid packing; Project Flyspeck;
%%% sphere packing",
%%% license = "public domain",
%%% supported = "no",
%%% docstring = "This is a bibliography about the Kepler
%%% Conjecture on optimal sphere packing, and
%%% recent advances in the general solid-body
%%% packing problem. More information about the
%%% Kepler Conjecture and its credible, but
%%% controversial, proof are given below.
%%%
%%% At version 1.33, the year coverage looked
%%% like this:
%%%
%%% 1611 ( 1) 1747 ( 0) 1883 ( 0)
%%% 1628 ( 0) 1764 ( 0) 1900 ( 1)
%%% 1629 ( 0) 1765 ( 0) 1901 ( 1)
%%% 1630 ( 0) 1766 ( 0) 1902 ( 1)
%%% 1632 ( 0) 1768 ( 0) 1904 ( 1)
%%% 1653 ( 0) 1789 ( 0) 1925 ( 1)
%%% 1680 ( 0) 1816 ( 0) 1952 ( 1)
%%% 1681 ( 0) 1817 ( 0) 1953 ( 2)
%%% 1686 ( 0) 1822 ( 0) 1958 ( 1)
%%% 1689 ( 0) 1825 ( 0) 1961 ( 1)
%%% 1690 ( 0) 1826 ( 0) 1962 ( 1)
%%% 1692 ( 0) 1828 ( 0) 1964 ( 2)
%%% 1694 ( 0) 1830 ( 0) 1966 ( 1)
%%% 1695 ( 0) 1831 ( 0) 1967 ( 3)
%%% 1696 ( 0) 1832 ( 0) 1968 ( 1)
%%% 1697 ( 0) 1833 ( 0) 1969 ( 1)
%%% 1698 ( 0) 1834 ( 0) 1970 ( 2)
%%% 1699 ( 0) 1835 ( 0) 1971 ( 1)
%%% 1700 ( 0) 1836 ( 0) 1972 ( 1)
%%% 1703 ( 0) 1839 ( 0) 1975 ( 1)
%%% 1707 ( 0) 1843 ( 0) 1979 ( 4)
%%% 1709 ( 0) 1845 ( 0) 1981 ( 2)
%%% 1710 ( 0) 1846 ( 0) 1982 ( 1)
%%% 1711 ( 0) 1847 ( 0) 1983 ( 2)
%%% 1712 ( 0) 1848 ( 0) 1984 ( 1)
%%% 1713 ( 0) 1849 ( 0) 1985 ( 3)
%%% 1716 ( 0) 1852 ( 0) 1988 ( 1)
%%% 1717 ( 0) 1853 ( 0) 1989 ( 2)
%%% 1718 ( 0) 1854 ( 0) 1990 ( 1)
%%% 1719 ( 0) 1855 ( 0) 1991 ( 4)
%%% 1720 ( 0) 1856 ( 0) 1992 ( 4)
%%% 1721 ( 0) 1857 ( 0) 1993 ( 11)
%%% 1722 ( 0) 1858 ( 0) 1994 ( 3)
%%% 1723 ( 0) 1859 ( 0) 1995 ( 4)
%%% 1724 ( 0) 1860 ( 0) 1996 ( 2)
%%% 1725 ( 0) 1861 ( 0) 1997 ( 7)
%%% 1726 ( 0) 1862 ( 0) 1998 ( 6)
%%% 1727 ( 0) 1863 ( 0) 1999 ( 10)
%%% 1728 ( 0) 1864 ( 0) 2000 ( 14)
%%% 1729 ( 0) 1865 ( 0) 2001 ( 13)
%%% 1730 ( 0) 1866 ( 0) 2002 ( 10)
%%% 1731 ( 0) 1867 ( 0) 2003 ( 8)
%%% 1732 ( 0) 1868 ( 0) 2004 ( 7)
%%% 1733 ( 0) 1869 ( 0) 2005 ( 11)
%%% 1734 ( 0) 1870 ( 0) 2006 ( 19)
%%% 1735 ( 0) 1871 ( 0) 2007 ( 13)
%%% 1736 ( 0) 1872 ( 0) 2008 ( 10)
%%% 1737 ( 0) 1873 ( 0) 2009 ( 11)
%%% 1738 ( 0) 1874 ( 0) 2010 ( 17)
%%% 1739 ( 0) 1875 ( 0) 2011 ( 10)
%%% 1740 ( 0) 1876 ( 0) 2012 ( 9)
%%% 1741 ( 0) 1877 ( 0) 2013 ( 10)
%%% 1742 ( 0) 1878 ( 0) 2014 ( 9)
%%% 1743 ( 0) 1879 ( 0) 2015 ( 2)
%%% 1744 ( 0) 1880 ( 0) 2016 ( 8)
%%% 1745 ( 0) 1881 ( 0) 2017 ( 3)
%%%
%%% Article: 183
%%% Book: 35
%%% InCollection: 17
%%% InProceedings: 19
%%% Misc: 3
%%% PhdThesis: 3
%%% Proceedings: 14
%%% TechReport: 2
%%% Unpublished: 1
%%%
%%% Total entries: 277
%%%
%%% A brief statement of the Kepler Conjecture
%%% (from page xvi of entry Conway:1999:SPL) is
%%% ``the so-called Kepler Conjecture [is that]
%%% no packing of three-dimensional spheres can
%%% have a greater density than that of the
%%% face-centered cubic lattice.''
%%%
%%% Proof of the Kepler Conjecture is problem
%%% number 15 (later 18) of David Hilbert's 1900
%%% list of 20 (later revised to 23) important
%%% mathematical problems for the 20th Century
%%% (see entries Hilbert:1900:MPV,
%%% Hilbert:1901:MPV, Hilbert:1902:MP, and
%%% Hilbert:2000:MP). [Some of those problems,
%%% though not that of the Kepler Conjecture, are
%%% included in the Clay Mathematics Institute
%%% Millennium Problem list for which validated
%%% solutions win a prize of one million US
%%% dollars.]
%%%
%%% Thomas C. Hales announced a proof of the
%%% Kepler Conjecture on 9 August 1998, so it
%%% should now be called the Kepler Theorem, but
%%% the proof was not published until 2005. See
%%% entry Morgan:2005:BRB for the reasons for the
%%% long delay in publication, and entry
%%% Hales:2000:CH for the prize-winning paper
%%% with a largely nonmathematical description of
%%% the nature of the problem.
%%%
%%% Hales' complicated proof is detailed in a
%%% book (entry Lagarias:2011:KCH), and discussed
%%% in nonmathematical form in two other books
%%% (entries Casti:2001:MMF and Szpiro:2003:KCH).
%%% The proof was also published in seven papers
%%% in a special journal issue (entries
%%% Hales:2006:SPIb, Toth:2006:GEF,
%%% Ferguson:2006:SPV, Hales:2006:SPV,
%%% Hales:2006:FKC, Hales:2006:HOK,
%%% Hales:2006:SPIa).
%%%
%%% Because of the great difficulty of the proof
%%% of the Kepler Conjecture, and the inability
%%% of other mathematicians to verify the proof,
%%% Hales began Project Flyspeck (see entry
%%% Hales:2008:FP) to produce a verification of
%%% the proof by a computer. Successful
%%% completion of that project was announced on
%%% various e-mail lists on 10-Aug-2014. Hales
%%% reported:
%%%
%%% ``The verification of all nonlinear
%%% inequalities in HOL Light on the
%%% Microsoft Azure cloud took approximately
%%% 5000 processor-hours. Almost all
%%% verifications were made in parallel with
%%% 32 cores, hence the real time is about
%%% 5000 / 32 = 156.25 hours. Nonlinear
%%% inequalities were verified with compiled
%%% versions of HOL Light and the
%%% verification tool developed in Solovyev's
%%% 2012 thesis.''
%%%
%%% The final report of that project appears in
%%% entry Hales:2015:FPK. Entry Adams:2014:FF
%%% discusses the proof, and the independent
%%% validation of the proof.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
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%%% ====================================================================
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@String{pub-NAP:adr = "Washington, DC, USA"}
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@String{pub-NORTON:adr = "New York, NY, USA"}
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@String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"}
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@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
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%%% ====================================================================
%%% Series abbreviations:
@String{ser-LNAI = "Lecture Notes in Artificial Intelligence"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
%%% ====================================================================
%%% Bibliography entries, sorted by increasing year and then by citation
%%% label within each year, with `bibsort -byyear':
@Book{Kepler:1611:SSN,
author = "Johannes Kepler",
title = "Strena, Seu, de Nive Sexangula",
publisher = "Godfrey Tampach",
address = "Frankfurt-am-Main, Germany",
year = "1611",
bibdate = "Wed Jan 09 08:37:25 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "This book contains the original formulation of the
now-famous Kepler Sphere Packing Conjecture. English
translation in \cite{Kepler:1966:SCS}.",
acknowledgement = ack-nhfb,
}
@Article{Hilbert:1900:MPV,
author = "David Hilbert",
title = "{Mathematische Probleme. Vortrag, gehalten auf dem
internationalen Mathematiker-Kongre{\ss} zu Paris
1900}. ({German}) [Mathematical Problems: Lecture held
at the {International Mathematicians Congress in Paris
1900}]",
journal = "G{\"o}tt. Nachr.",
volume = "??",
number = "??",
pages = "253--297",
month = "????",
year = "1900",
bibdate = "Wed Jan 09 12:29:52 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "This is the paper in which Hilbert lays out his
now-famous list of 20 (revised to 23 in 1901)
challenging problems for mathematicians to address in
the 20th Century. Reprinted in \cite{Hilbert:1901:MPV}.
English translation in
\cite{Hilbert:1902:MP,Hilbert:2000:MP}",
ZMnumber = "JFM 31.0068.03",
acknowledgement = ack-nhfb,
keywords = "Hilbert's 20 Problems",
language = "German",
remark = "The problems are (in German): \\
1. Cantor's Problem von der M{\"a}chtigkeit des
Continuums \\
2. Die Widerspruchslosigkeit der arithmetischen Axiome
\\
3. Die Volumengleichheit zweier Tetraeder von gleicher
Grundfl{\"a}che und H{\"o}he (Unm{\"o}glichkeit des
Beweises durch Zerlegung in congruente Teile) \\
4. Problem von der Geraden als k{\"u}rzester Verbindung
zweier Punkte \\
5. Mathematische Behandlung der Axiome der Physik \\
6. Irrationalit{\"a}t und Transcendenz bestimmter
Zahlen (z. B. $ \pi $, $ \sqrt {2} $, and $e$ (??)) \\
7. Primzahlenprobleme \\
8. Beweis des allgemeinsten Reciprocit{\"a}tsgesetzes
im beliebigen Zahlk{\"o}rper \\
9. Entscheidung der L{\"o}sbarkeit einer diophantischen
Gleichung \\
10. Ausdehnung des Kronecker'schen Satzes {\"u}ber
Abel'sche K{\"o}rper auf einen beliebigen algebraischen
Rationalit{\"a}tsbereich \\
11. Unm{\"o}glichkeit der L{\"o}sung der allgemeinen
Gleichung \\
7. Grades mittels Functionen von nur zwei Argumenten
\\
12. Strenge Begr{\"u}ndung von Schubert's
Abz{\"a}hlungscalc{\"u}l \\
13. Problem der Topologie algebraischer Curven und
Fl{\"a}chen \\
14. Darstellung definiter Formen durch Quadrate \\
15. Aufbau des Raumes aus congruenten Polyedern \\
16. Sind die L{\"o}sungen regul{\"a}rer
Variationsprobleme stets notwendig analytisch? \\
17. Allgemeines Randwertproblem \\
18. Beweis der Existenz linearer
Differentialgleichungen mit vorgeschriebener
Monodromiegruppe \\
19. Uniformisirung analytischer Beziehungen mittels
automorpher Functionen \\
20. Weiterf{\"u}hrung der Methoden der
Variationsrechnung \\
(Rough) English translations of the problem titles are:
\\
1. Cantor's problem of the thickness of continua \\
2. The consistency of the axioms of arithmetic \\
3. The volume equality of two tetrahedra of equal base
and height (impossibility of proof by breaking it down
into congruent parts) \\
4. Problem of the straight line as a short connection
of two points \\
5. Mathematical treatment of the axioms of physics \\
6. Irrationality and transcendence of certain numbers
(such as $ \pi $, $ \sqrt {2}$, and $e$ (??)) \\
7 Prime problems \\
8. Evidence of the most common reciprocity theorem in
the numbers \\
9. Decision of the solvability of a Diophantine
equation \\
10. Expansion of the Kronecker set over Abelian bodies
on any algebraic rational area \\
11. Inability to solve the general equation of 7th
degree by means of functions of two arguments \\
12. Rigorous justification of Schubert's counting
calculus \\
13. Issue of the topology of algebraic curves and
surfaces \\
14. Representation of definite forms by squares \\
15. Construction of space from congruent polyhedra \\
16. Are the regular variation problems solutions always
necessary analytic? \\
17. General boundary value problem \\
18. Evidence of the existence of linear differential
equations with prescribed Monodromiegruppe \\
19. Uniformization of analytic relations by means of
automorphic functions \\
20. Continuation of the methods of the calculus of
variations",
}
@Article{Hilbert:1901:MPV,
author = "David Hilbert",
title = "{Mathematische Probleme. Vortrag, gehalten auf dem
internationalen Mathematiker-Kongre{\ss} zu Paris
1900}. ({German}) [Mathematical Problems: Lecture held
at the {International Mathematicians Congress in Paris
1900}]",
journal = "Arch. d. Math. u. Phys",
volume = "3",
number = "1",
pages = "44--63, 213--237",
month = "????",
year = "1901",
DOI = "",
bibdate = "Wed Jan 09 09:37:38 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "",
ZMnumber = "JFM 32.0084.05",
acknowledgement = ack-nhfb,
ajournal = "Arch. Math. Phys.",
keywords = "Hilbert's 23 Problems",
language = "German",
}
@Article{Hilbert:1902:MP,
author = "David Hilbert",
title = "Mathematical Problems",
journal = j-BULL-AMS,
volume = "8",
number = "10",
pages = "437--479",
month = "????",
year = "1902",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1902-00923-3",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRnumber = "1557926",
bibdate = "Wed Jan 09 17:25:01 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "English translation of Hilbert's famous list of 23
important problems in mathematics for the 20th
Century.",
URL = "http://www.ams.org/journals/bull/1902-08-10/S0002-9904-1902-00923-3/S0002-9904-1902-00923-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
keywords = "Hilbert's 23 Problems",
}
@Article{Minkowski:1904:DGL,
author = "H. Minkowski",
title = "{Dichteste gitterf{\"o}rmige Lagerung kongruenter
K{\"o}rper}. ({German}) [{Closest} lattice packing of
congruent bodies]",
journal = "Nachr. K. Ges. Wiss. G{\"o}ttingen",
volume = "??",
number = "??",
pages = "311--355",
month = "????",
year = "1904",
DOI = "",
bibdate = "Wed Jan 09 09:43:51 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "The `proof' of a packing theorem in this paper was
later shown to be wrong; see \cite[pages
1543--1544]{Lagarias:2012:MPR}",
URL = "",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Struik:1925:PIL,
author = "D. J. Struik",
title = "Het Probleem {``De impletione loci''}. ({Dutch})
[{The} problem {``On Local Filling''}]",
journal = "Nieuw Archief voor Wiskunde, Series 2",
volume = "15",
number = "??",
pages = "121--137",
year = "1925--1928",
DOI = "",
bibdate = "Wed Jan 09 09:56:24 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "",
acknowledgement = ack-nhfb,
language = "Dutch",
}
@Book{Weyl:1952:S,
author = "Hermann Weyl",
title = "Symmetry",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "168",
year = "1952",
ISBN = "0-691-08045-3",
ISBN-13 = "978-0-691-08045-1",
LCCN = "",
bibdate = "Wed Jan 09 15:33:17 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
author-dates = "1885--1955",
}
@Article{Schutte:1953:PDK,
author = "K. Sch{\"u}tte and B. L. van der Waerden",
title = "{Das Problem der dreizehn Kugeln}. ({German}) [{The}
problem of thirteen bullets]",
journal = j-MATH-ANN,
volume = "125",
number = "??",
pages = "325--334",
month = "????",
year = "1953",
CODEN = "MAANA3",
DOI = "https://doi.org/10.1007/BF01343127",
ISSN = "0025-5831 (print), 1432-1807 (electronic)",
ISSN-L = "0025-5831",
MRclass = "52.0X",
MRnumber = "0053537 (14,787e)",
MRreviewer = "H. S. M. Coxeter",
bibdate = "Wed Jan 09 09:48:48 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.com/article/10.1007/BF01343127",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Annalen",
language = "German",
}
@Book{Toth:1953:LEK,
author = "L. Fejes T{\'o}th",
title = "{Lagerungen in der Ebene, auf der Kugeln und im Raum}.
({German}) [{Ball} deposits in the plane and in
space]",
volume = "65",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 197",
year = "1953",
LCCN = "",
MRclass = "52.0X",
MRnumber = "0057566 (15,248b)",
MRreviewer = "W. O. Moser",
bibdate = "Wed Jan 09 09:16:25 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "See also second edition \cite{Toth:1972:LEK}.",
series = "{Grundlehren der mathematischen Wissenschaften in
Einzeldarstellungen mit besonderer Ber{\"u}cksichtigung
der Anwendungsgebiete}",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Renyi:1958:ODP,
author = "A. R{\'e}nyi",
title = "On a one-dimensional problem concerning random space
filling",
journal = "Magyar Tud. Akad. Mat. Kutat{\'o} Int. K{\"o}zl.",
volume = "3",
number = "1--2",
pages = "109--127",
month = "????",
year = "1958",
MRclass = "60.00",
MRnumber = "0104284 (21 \#3039)",
MRreviewer = "P. Erd{\H{o}}s",
bibdate = "Wed Feb 29 21:10:40 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
acknowledgement = ack-nhfb,
xxjournal = "Publ. Math. Inst. Hung. Acad. Sci.",
}
@Article{Higuti:1961:SSR,
author = "Isao Higuti",
title = "A statistical study of random packing of unequal
spheres",
journal = j-ANN-INST-STAT-MATH-TOKYO,
volume = "12",
number = "3",
pages = "257--271",
month = oct,
year = "1961",
CODEN = "AISXAD",
DOI = "https://doi.org/10.1007/BF01728935",
ISSN = "0020-3157 (print), 1572-9052 (electronic)",
ISSN-L = "0020-3157",
bibdate = "Sat Jan 31 16:59:46 MST 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.com/article/10.1007/BF01728935",
acknowledgement = ack-nhfb,
fjournal = "Annals of the Institute of Statistical Mathematics",
journal-URL = "http://link.springer.com/journal/10463",
}
@Article{Groemer:1962:BDG,
author = "H. Groemer",
title = "{{\"U}ber die dichteste gitterf{\"o}rmige Lagerung
kongruenter Tetraeder}. ({German}) [On the densest
lattice storage of congruent tetrahedra]",
journal = j-MONAT-MATH,
volume = "66",
number = "??",
pages = "12--15",
month = "????",
year = "1962",
CODEN = "MNMTA2",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
MRclass = "52.45 (10.25)",
MRnumber = "0139077 (25 \#2516)",
MRreviewer = "T. Estermann",
bibdate = "Wed Jan 09 09:25:04 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
language = "German",
}
@Article{Leech:1964:SSP,
author = "John Leech",
title = "Some sphere packings in higher space",
journal = j-CAN-J-MATH,
volume = "16",
number = "??",
pages = "657--682",
month = "????",
year = "1964",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1964-065-1",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:33 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v16/;
http://www.math.utah.edu/pub/tex/bib/canjmath1960.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
}
@Book{Rogers:1964:PC,
author = "C. A. (Claude Ambrose) Rogers",
title = "Packing and covering",
volume = "54",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "viii + 111",
year = "1964",
LCCN = "QA248 .R64",
MRclass = "52.45",
MRnumber = "0172183 (30 \#2405)",
MRreviewer = "R. P. Bambah",
bibdate = "Wed Jan 9 09:48:56 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Cambridge tracts in mathematics and mathematical
physics",
acknowledgement = ack-nhfb,
subject = "Generalized spaces",
}
@Book{Kepler:1966:SCS,
editor = "Johannes Kepler",
title = "The six-cornered snowflake",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvi + 75",
year = "1966",
ISBN = "020",
ISBN-13 = "020",
LCCN = "QC929.S7 K413",
bibdate = "Wed Jan 9 08:38:36 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated from the Latin by Colin Hardie, with essays
by L. L. Whyte and B. F. J. Mason. Text in Latin with
English translation on facing page. Notes and
commentaries in English. Originally published in
\cite{Kepler:1611:SSN}.",
price = "21/-",
acknowledgement = ack-nhfb,
author-dates = "1571--1630",
subject = "Snowflakes; Early works to 1800",
}
@Article{Leech:1967:FDN,
author = "John Leech",
title = "Five dimensional non-lattice sphere packings",
journal = j-CAN-MATH-BULL,
volume = "10",
number = "??",
pages = "387--394",
month = "????",
year = "1967",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1967-037-5",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
bibdate = "Thu Sep 8 10:03:24 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v10/;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
}
@Article{Leech:1967:NSP,
author = "John Leech",
title = "Notes on sphere packings",
journal = j-CAN-J-MATH,
volume = "19",
number = "??",
pages = "251--267",
month = "????",
year = "1967",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1967-017-0",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:36 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v19/;
http://www.math.utah.edu/pub/tex/bib/canjmath1960.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
}
@InProceedings{Solomon:1967:RPD,
author = "H. Solomon",
editor = "Lucien M. {Le Cam} and Jerzy Neyman",
booktitle = "{Proceedings of the Fifth Berkeley Symposium on
Mathematical Statistics and Probability. Volume III.
Physical Sciences}",
title = "Random packing density",
volume = "3",
publisher = pub-U-CAL,
address = pub-U-CAL:adr,
pages = "119--134",
year = "1967",
LCCN = "QA276 .B4 v.3",
bibdate = "Wed Feb 29 21:12:50 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Held at the Statistical Laboratory, University of
California, June 21--July 18, 1965 and December 27,
1965--January 7, 1966.",
URL = "http://projecteuclid.org/euclid.bsmsp/1200513624",
acknowledgement = ack-nhfb,
}
@Book{Rogers:1968:UPR,
author = "Claude Ambrose Rogers",
title = "{Ukladki i pokrytije}. ({Russian}) [Laying and
covering]",
publisher = "????",
address = "????",
pages = "134",
year = "1968",
LCCN = "QA611 .R6317",
bibdate = "Wed Jan 9 09:48:56 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1920--",
language = "Russian",
subject = "Generalized spaces",
xxnote = "Find original Russian title and check likely-garbled
transliteration.",
}
@Article{Leech:1969:SSD,
author = "John Leech",
title = "Six and seven dimensional non-lattice sphere
packings",
journal = j-CAN-MATH-BULL,
volume = "12",
number = "??",
pages = "151--156",
month = "????",
year = "1969",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1969-014-1",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
bibdate = "Thu Sep 8 10:03:37 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v12/;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
}
@Article{Blaisdell:1970:RSP,
author = "B. E. Blaisdell and H. Solomon",
title = "On random sequential packing in the plane and a
conjecture of {Pal{\'a}sti}",
journal = j-J-APPL-PROBAB,
volume = "7",
number = "3",
pages = "667--689",
month = dec,
year = "1970",
CODEN = "JPRBAM",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
bibdate = "Wed Feb 29 21:17:55 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.jstor.org/stable/3211946",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html",
}
@Article{Hoylman:1970:DLP,
author = "D. J. Hoylman",
title = "The densest lattice packing of tetrahedra",
journal = j-BULL-AMS,
volume = "76",
number = "??",
pages = "135--137",
month = "????",
year = "1970",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Fri Aug 14 17:28:05 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Leech:1971:SPE,
author = "John Leech and N. J. A. Sloane",
title = "Sphere packings and error-correcting codes",
journal = j-CAN-J-MATH,
volume = "23",
number = "??",
pages = "718--745",
month = "????",
year = "1971",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1971-081-3",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:42 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v23/;
http://www.math.utah.edu/pub/tex/bib/canjmath1970.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
}
@Book{Toth:1972:LEK,
author = "L. Fejes T{\'o}th",
title = "{Lagerungen in der Ebene, auf der Kugeln und im Raum}.
({German}) [{Ball} deposits in the plane and in
space]",
volume = "65",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xi + 238",
year = "1972",
ISBN = "3-540-05477-4",
ISBN-13 = "978-3-540-05477-1",
LCCN = "",
MRclass = "52.0X",
MRnumber = "0057566 (15,248b)",
MRreviewer = "W. O. Moser",
bibdate = "Wed Jan 09 09:16:25 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "See also first edition \cite{Toth:1953:LEK}.",
series = "{Grundlehren der mathematischen Wissenschaften in
Einzeldarstellungen mit besonderer Ber{\"u}cksichtigung
der Anwendungsgebiete}",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Akeda:1975:NTP,
author = "Y. Akeda and M. Hori",
title = "Numerical test of {Pal{\'a}sti}'s conjecture on
two-dimensional random packing density",
journal = j-NATURE,
volume = "254",
number = "5498",
pages = "318--319",
day = "27",
month = mar,
year = "1975",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/254318a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Feb 29 21:19:24 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.nature.com/nature/journal/v254/n5498/pdf/254318a0.pdf",
abstract = "Random packing and random space-filling problems have
received frequent attention. In one dimension, this
topic is usually called the car-parking problem.
Pal{\'a}sti generalised the parking problem to two
dimensions and conjectured that the random packing
density in the two-dimensional case is equal to the
square of that in the one-dimensional case. Here we
provide a thorough check on her conjecture and confirm
its validity.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
}
@Article{Gilbert:1979:PPT,
author = "E. N. Gilbert",
title = "The Packing Problem for Twisted Pairs",
journal = j-BELL-SYST-TECH-J,
volume = "58",
number = "10",
pages = "2143--2162",
month = dec,
year = "1979",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1979/BSTJ.1979.5810.html;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol58/bstj58-10-2143.pdf",
abstract = "When wires are packed together in a bundle, as in a
cable or on a shelf of a main distribution frame, the
packing fraction $f$ is the fraction of cross-sectional
area of the bundle occupied by wire. With wires all the
same radius, packing fractions as high as $ 0.90690$
can be achieved. However, when the wires are pairs that
have been twisted to avoid crosstalk, the packing
fraction is much smaller. The largest obtainable
packing fraction depends on other properties of the
packing. For example, with pairs twisted by machine,
all pairs twist at the same rate, and that influences
the packing fraction. Several packing problems are
considered, but most attention is given to a
particularly regular kind of packing in which pairs
twist about straight parallel axes located in a lattice
arrangement. The densest lattice packing has packing
fraction $ 0.56767$. The densest lattice is a
complicated one in which each wire touches $ 10$ wires
belonging to $6$ other pairs. The numbers $ 10$ and $6$
cannot be increased even with nonlattice packings of
pairs with straight parallel axes. These other packings
are also conjectured to have packing fractions less
than $ 0.56767$, although only $ f < 0.62240$ is
proved.",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Book{Schrijver:1979:PCC,
author = "A. Schrijver",
title = "Packing and covering in combinatorics",
volume = "106",
publisher = "Mathematisch Centrum",
address = "Amsterdam, The Netherlands",
pages = "313",
year = "1979",
ISBN = "90-6196-180-7",
ISBN-13 = "978-90-6196-180-2",
LCCN = "QA166.7 .P32",
bibdate = "Wed Jan 9 09:48:56 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematical centre tracts",
acknowledgement = ack-nhfb,
subject = "Combinatorial packing and covering",
}
@Article{Tanemura:1979:RCP,
author = "M. Tanemura",
title = "On random complete packing by discs",
journal = j-ANN-INST-STAT-MATH-TOKYO,
volume = "31",
number = "Part B",
pages = "351--365",
month = "????",
year = "1979",
CODEN = "AISXAD",
ISSN = "0020-3157 (print), 1572-9052 (electronic)",
ISSN-L = "0020-3157",
bibdate = "Wed Feb 29 21:24:06 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of the Institute of Statistical Mathematics
(Tokyo)",
}
@PhdThesis{Thompson:1979:ECC,
author = "Thomas Miller Thompson",
title = "From error-correcting codes through sphere packings to
simple groups",
type = "Thesis ({Ph.D.})",
school = "Department of Mathematics, University of California,
Davis",
address = "Davis, CA, USA",
pages = "250",
year = "1979",
LCCN = "LD781.D5j 1979 T566",
bibdate = "Thu Aug 13 18:08:02 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations, academic --- University of California,
Davis --- mathematics",
}
@Article{Senechal:1981:WTF,
author = "Marjorie Senechal",
title = "Which tetrahedra fill space?",
journal = j-MATH-MAG,
volume = "54",
number = "5",
pages = "227--243",
month = "????",
year = "1981",
CODEN = "MAMGA8",
DOI = "https://doi.org/10.2307/2689983",
ISSN = "0025-570X",
MRclass = "52A45 (01A05 05B45 52-03 52A25)",
MRnumber = "644075 (83h:52020)",
MRreviewer = "A. Florian",
bibdate = "Wed Jan 09 09:54:58 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@Article{Sloane:1981:TSP,
author = "Neil J. A. Sloane",
title = "Tables of sphere packings and spherical codes",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "27",
number = "3",
pages = "327--338",
month = mar,
year = "1981",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/TIT.1981.1056351",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Thu Aug 13 17:46:36 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/tit/tit27.html#Sloane81;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
}
@Book{Weyl:1982:S,
author = "Hermann Weyl",
title = "Symmetry",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "168",
year = "1982",
ISBN = "0-691-02374-3",
ISBN-13 = "978-0-691-02374-8",
LCCN = "",
bibdate = "Wed Jan 09 15:33:17 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
author-dates = "1885--1955",
remark = "Reprint of \cite{Weyl:1952:S}.",
}
@Article{Bagchi:1983:TAA,
author = "Bagchi and Cerjan and Stuart A. Rice",
title = "Theoretical analysis of the achievement of random
close packing of hard spheres and a conjecture on
spinodal decomposition",
journal = j-PHYS-REV-B-CMMP,
volume = "28",
pages = "6411",
year = "1983",
CODEN = "PRBMDO",
ISSN = "1098-0121",
ISSN-L = "1098-0121",
bibdate = "Thu Aug 13 18:08:02 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review B: Condensed Matter and Materials Physics",
journal-URL = "http://prb.aps.org/browse",
keywords = "spin, theoretical",
}
@Book{Thompson:1983:ECC,
author = "Thomas M. Thompson",
title = "From error-correcting codes through sphere packings to
simple groups",
volume = "21",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "xiv + 228",
year = "1983",
ISBN = "0-88385-023-0",
ISBN-13 = "978-0-88385-023-7",
LCCN = "QA268 .T56 1983",
bibdate = "Thu Aug 13 18:08:02 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Carus mathematical monographs",
acknowledgement = ack-nhfb,
keywords = "error-correcting codes (information theory); finite
simple groups",
}
@Article{Sloane:1984:PS,
author = "N. J. A. Sloane",
title = "The packing of spheres",
journal = j-SCI-AMER,
volume = "250",
number = "1",
pages = "92--101",
month = jan,
year = "1984",
CODEN = "SCAMAC",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Thu Aug 13 18:08:02 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
classification = "A0550 (Lattice theory and statistics; Ising
problems)",
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
keywords = "digital signalling; lattice theory and statistics;
sphere packing",
treatment = "T Theoretical or Mathematical",
}
@Article{Jodrey:1985:CSC,
author = "W. S. Jodrey and E. M. Tory",
title = "Computer simulation of close random packing of equal
spheres",
journal = j-PHYS-REV-A,
volume = "32",
number = "4",
pages = "2347--2351",
month = oct,
year = "1985",
CODEN = "PLRAAN",
DOI = "https://doi.org/10.1103/PhysRevA.32.2347",
ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
ISSN-L = "1050-2947",
bibdate = "Thu Aug 13 17:43:15 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevA.32.2347",
acknowledgement = ack-nhfb,
fjournal = "Physical Review A (Atomic, Molecular, and Optical
Physics)",
journal-URL = "http://pra.aps.org/browse",
}
@InProceedings{Marsaglia:1985:CVR,
author = "George Marsaglia",
title = "A Current View of Random Number Generators",
crossref = "Billard:1985:CSS",
pages = "3--10",
year = "1985",
bibdate = "Thu Dec 18 13:39:28 2003",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://stat.fsu.edu/pub/diehard/;
http://www.evensen.org/marsaglia/keynote.ps",
acknowledgement = ack-nhfb,
remark = "This paper introduces the Parking Lot test used in the
Diehard Battery test suite.",
}
@Book{Conway:1988:SPL,
author = "John Horton Conway and N. J. A. (Neil James Alexander)
Sloane and others",
title = "Sphere Packings, Lattices and Groups",
volume = "290",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxvii + 663",
year = "1988",
ISBN = "0-387-96617-X",
ISBN-13 = "978-0-387-96617-5",
LCCN = "QA166.7 .C66 1988; QA3 .G75; QA3 .G7; QA166.7 .C66
1988",
bibdate = "Thu Aug 13 18:08:02 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
melvyl.cdlib.org:210/CDL90",
price = "US\$45.00",
series = "{Grundlehren der mathematischen Wissenschaften}",
acknowledgement = ack-nhfb,
keywords = "book; c1988; c198x; c19xx; codes; constant; constants;
G1; G2; group; John Conway; laminated; lattice;
packing; polytope; polytopes; quantization; text;
zz06099",
subject = "Combinatorial packing and covering; Sphere; Lattice
theory; Finite groups",
}
@Article{Toth:1989:FSP,
author = "G{\'a}bor Fejes T{\'o}th and Peter Gritzmann and J. M.
Wills",
title = "Finite Sphere Packing and Sphere Covering",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "4",
number = "1",
pages = "19--40",
month = dec,
year = "1989",
CODEN = "DCGEER",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Thu Aug 13 17:47:55 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg4.html#TothGW89;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Book{Weyl:1989:S,
author = "Hermann Weyl",
title = "Symmetry",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "168",
year = "1989",
ISBN = "0-691-02374-3",
ISBN-13 = "978-0-691-02374-8",
LCCN = "",
bibdate = "Wed Jan 09 15:33:17 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
author-dates = "1885--1955",
remark = "Reprint of \cite{Weyl:1952:S}.",
}
@Article{Kuperberg:1990:DLP,
author = "G. Kuperberg and W. Kuperberg",
title = "Double-lattice packings of convex bodies in the
plane",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "5",
number = "1",
pages = "389--397",
month = dec,
year = "1990",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/BF02187800",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52A45",
MRnumber = "1043721 (90k:52027)",
MRreviewer = "R. Blind",
bibdate = "Wed Jan 09 09:42:32 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Bezdek:1991:MDS,
author = "Andr{\'a}s Bezdek and Wlodzimierz Kuperberg and E.
Makai",
title = "Maximum Density Space Packing with Parallel Strings of
Spheres",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "6",
number = "1",
pages = "277--283",
month = dec,
year = "1991",
CODEN = "DCGEER",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Thu Aug 13 17:49:09 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg6.html#BezdekKM91;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Clare:1991:OPC,
author = "B. W. Clare and D. L. Kepert",
title = "The optimal packing of circles on a sphere",
journal = j-J-MATH-CHEM,
volume = "6",
number = "1",
pages = "325--349",
month = dec,
year = "1991",
CODEN = "JMCHEG",
DOI = "https://doi.org/10.1007/BF01192589",
ISSN = "0259-9791 (print), 1572-8897 (electronic)",
ISSN-L = "0259-9791",
bibdate = "Fri Apr 10 06:38:59 MDT 2015",
bibsource = "http://link.springer.com/journal/10910/6/1;
http://www.math.utah.edu/pub/tex/bib/jmathchem.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.com/article/10.1007/BF01192589",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Chemistry",
journal-URL = "http://link.springer.com/journal/10910",
journalabr = "J. Math. Chem.",
}
@TechReport{Haussler:1991:SPN,
author = "David Haussler",
title = "Sphere Packing numbers for subsets of the {Boolean}
{$N$}-cube with bounded {Vapnik--Chervonenkis}
dimension",
number = "UCSC-CRL-91-41",
institution = "University of California, Santa Cruz",
address = "Santa Cruz, CA, USA",
pages = "14",
month = oct,
year = "1991",
bibdate = "Thu Aug 13 18:07:58 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "ftp://ftp.cse.ucsc.edu/pub/tr/ucsc-crl-91-41.ps.Z;
mailto:rnalib@ftp.cs.ucsc.edu",
abstract = "Let V contained in $ \lbrace $0,1$ \rbrace ${\^{}}n
have Vapnk-Chervonenkis dimension d. Let M(k/n,V)
denote the cardinality of the largest W contained in V
such that any two distinct vectors in W differ on at
least k indices. We show that M(k/n,V) $<$ =
(cn/(k+d)){\^{}}d for some constant c. This improves on
the previous best result of ((cn/k)log(n/k)){\^{}}d.
This new result has applications in the theory of
empirical processes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Max:1991:CAS,
author = "Nelson L. Max",
booktitle = "IEEE Visualization",
title = "Computer Assisted Sphere Packing in Higher
Dimensions",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "102--108",
year = "1991",
bibdate = "Thu Aug 13 17:48:35 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/visualization/visualization1991.html#Max91;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Coffman:1992:PAP,
author = "E. G. {Coffman, Jr.} and D. S. Johnson and P. W.
Shor",
title = "Probabilistic Analysis of Packing and Related
Partitioning Problems",
crossref = "Steele:1992:PA",
chapter = "7",
pages = "87--108",
year = "1992",
bibdate = "Wed Jan 09 18:20:11 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Article{Hales:1992:SPP,
author = "Thomas C. Hales",
title = "The sphere packing problem",
journal = j-J-COMPUT-APPL-MATH,
volume = "44",
number = "1",
pages = "41--76",
day = "9",
month = dec,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:56 MST 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279290052Y",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InCollection{Berger:1993:PC,
author = "Marcel Berger",
booktitle = "Differential geometry and topology ({Alghero}, 1992)",
title = "Les paquets de cercles. ({French}) [{Circle}
packing]",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "23--64",
year = "1993",
MRclass = "52C15 (52C17)",
MRnumber = "1339286 (96e:52043)",
MRreviewer = "Igor Rivin",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
language = "French",
}
@Book{Conway:1993:SPL,
author = "John Horton Conway and N. J. A. (Neil James Alexander)
Sloane and others",
title = "Sphere packings, lattices, and groups",
volume = "290",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xliii + 679",
year = "1993",
ISBN = "0-387-97912-3, 3-540-97912-3",
ISBN-13 = "978-0-387-97912-0, 978-3-540-97912-8",
LCCN = "QA166.7 .C66 1993",
bibdate = "Thu Aug 13 17:40:44 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "{Grundlehren der mathematischen Wissenschaften}",
acknowledgement = ack-nhfb,
subject = "combinatorial packing and covering; sphere packings;
lattice theory; finite groups",
}
@Article{Hales:1993:RDS,
author = "Thomas C. Hales",
title = "Remarks on the density of sphere packings in three
dimensions",
journal = j-COMBINATORICA,
volume = "13",
number = "2",
pages = "181--197",
year = "1993",
CODEN = "COMBDI",
ISSN = "0209-9683 (print), 1439-6912 (electronic)",
ISSN-L = "0209-9683",
bibdate = "Thu Aug 13 17:49:58 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/combinatorica/combinatorica13.html#Hales93;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Combinatorica",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/493",
}
@InCollection{Hsiang:1993:GS,
author = "Wu-Yi Hsiang",
booktitle = "Differential geometry ({Shanghai}, 1991)",
title = "The geometry of spheres",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "92--107",
year = "1993",
MRclass = "52C17",
MRnumber = "1341602 (97f:52028)",
MRreviewer = "J. B{\"o}hm",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hsiang:1993:SPPa,
author = "Wu-Yi Hsiang",
title = "On the sphere packing problem and the proof of
{Kepler's Conjecture}",
journal = j-INT-J-MATH,
volume = "4",
number = "5",
pages = "739--831",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1142/S0129167X93000364",
ISSN = "0129-167X",
MRclass = "52C17",
MRnumber = "1245351 (95g:52032)",
MRreviewer = "G{\'a}bor Fejes T{\'o}th",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics",
keywords = "Kepler sphere-packing conjecture",
}
@InCollection{Hsiang:1993:SPPb,
author = "Wu-Yi Hsiang",
booktitle = "Differential geometry and topology ({Alghero, 1992})",
title = "On the sphere packing problem and the proof of
{Kepler's Conjecture}",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "117--127",
year = "1993",
MRclass = "52C17",
MRnumber = "1339290 (96f:52028)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Kunyavskii:1992:SPC,
author = "Boris {\`E}. Kunyavskii",
title = "Sphere packings centered at {$S$}-units of algebraic
tori",
journal = j-LECT-NOTES-MATH,
volume = "1518",
pages = "108--121",
year = "1992",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0087996",
ISBN = "3-540-55651-6 (print), 3-540-47267-3 (e-book)",
ISBN-13 = "978-3-540-55651-0 (print), 978-3-540-47267-4
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "11H31 (11T71 52C07)",
MRnumber = "1186419 (93i:11077)",
MRreviewer = "Simon N. Litsyn",
bibdate = "Fri May 9 19:07:24 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1990.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0087996/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0087986",
book-URL = "http://www.springerlink.com/content/978-3-540-47267-4",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Mathe:1993:KG,
author = "Katalin Bogn{\'a}r M{\'a}th{\'e}",
title = "{{\"U}ber Kugelsysteme unter
Ger{\"a}umigkeitsbedingungen}. ({German}) [{On} sphere
systems under spaciousness conditions]",
journal = "Studia Sci. Math. Hungar.",
volume = "28",
number = "3-4",
pages = "431--445",
year = "1993",
CODEN = "SSMHAX",
ISSN = "0081-6906",
MRclass = "52C17",
MRnumber = "1266827 (95b:52032)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Studia Scientiarum Mathematicarum Hungarica. A
Quarterly of the Hungarian Academy of Sciences",
keywords = "Kepler sphere-packing conjecture",
language = "German",
}
@Article{Muder:1993:NBL,
author = "Douglas J. Muder",
title = "A New Bound on the Local Density of Sphere Packings",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "10",
number = "1",
pages = "351--375",
month = dec,
year = "1993",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/BF02573984",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "1243334 (94h:52041)",
MRreviewer = "N. J. A. Sloane",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg10.html#Muder93;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Szirmai:1993:OSP,
author = "Jen{\H{o}} Szirmai",
title = "Optimal sphere packings under some space groups",
journal = "Alkalmaz. Mat. Lapok",
volume = "17",
number = "1--2",
pages = "87--99 (1994)",
year = "1993",
ISSN = "0133-3399",
MRclass = "52C17",
MRnumber = "1336186 (96g:52038)",
MRreviewer = "B{\'e}la Uhrin",
bibdate = "Thu Apr 12 18:15:04 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Alkalmazott Matematikai Lapok",
}
@InCollection{Toth:1993:PCC,
author = "G. Fejes T{\'o}th and W. Kuperberg",
title = "Packing and covering with convex sets",
crossref = "Gruber:1993:HCG",
volume = "B",
pages = "799--860",
year = "1993",
bibdate = "Wed Jan 09 09:09:31 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Article{Hales:1994:SKC,
author = "Thomas C. Hales",
title = "The status of the {Kepler Conjecture}",
journal = j-MATH-INTEL,
volume = "16",
number = "3",
pages = "47--58",
year = "1994",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF03024356",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "52C17",
MRnumber = "1281754 (95g:52033)",
MRreviewer = "G{\'a}bor Fejes T{\'o}th",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hsiang:1994:GS,
author = "Wu-Yi Hsiang",
title = "The geometry of spheres",
journal = j-NORMAT,
volume = "42",
number = "1",
pages = "1--12",
year = "1994",
ISSN = "0801-3500",
MRclass = "52C17 (51M25)",
MRnumber = "1278230 (95f:52028)",
MRreviewer = "W. J. Firey",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Normat. Nordisk Matematisk Tidskrift",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Zinchenko:1994:ARC,
author = "Alexander Z. Zinchenko",
title = "Algorithm for Random Close Packing of Spheres with
Periodic Boundary Conditions",
journal = j-J-COMPUT-PHYS,
volume = "114",
number = "2",
pages = "298--307",
month = oct,
year = "1994",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1994.1168",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:54:57 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999184711685",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Book{Brackenridge:1995:KND,
author = "J. Bruce Brackenridge",
title = "The key to {Newton}'s dynamics: the {Kepler} problem
and the {Principia}: containing an {English}
translation of sections 1, 2, and 3 of book one from
the first (1687) edition of {Newton}'s {Mathematical
Principles of Natural Philosophy}",
publisher = pub-U-CAL,
address = pub-U-CAL:adr,
pages = "xiii + 299",
year = "1995",
ISBN = "0-520-20065-9 (hardcover), 0-520-20217-1 (paperback)",
ISBN-13 = "978-0-520-20065-4 (hardcover), 978-0-520-20217-7
(paperback)",
LCCN = "QB355 .B694 1995",
bibdate = "Thu Aug 13 16:26:27 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/ucal051/95032978.html;
http://www.loc.gov/catdir/description/ucal041/95032978.html",
acknowledgement = ack-nhfb,
subject = "Kepler's laws; celestial mechanics",
}
@Article{Conway:1995:WAB,
author = "John H. Conway and Neil J. A. Sloane",
title = "What are All the Best Sphere Packings in Low
Dimensions?",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "13",
number = "1",
pages = "383--403",
month = dec,
year = "1995",
CODEN = "DCGEER",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Thu Aug 13 17:51:55 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg13.html#ConwayS95;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Haussler:1995:SPN,
author = "David Haussler",
title = "Sphere Packing Numbers for Subsets of the {Boolean}
$n$-Cube with Bounded {Vapnik--Chervonenkis}
Dimension",
journal = j-J-COMB-THEORY-A,
volume = "69",
number = "2",
pages = "217--232",
year = "1995",
CODEN = "JCBTA7",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
bibdate = "Thu Aug 13 17:52:38 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/jct/jcta69.html#Haussler95;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory (Series A)",
}
@Article{Hsiang:1995:RCH,
author = "Wu-Yi Hsiang",
title = "A rejoinder to {T. C. Hales}'s article: {``The status
of the Kepler Conjecture'' [Math.\ Intelligencer {\bf
16} (1994), no. 3, 47--58; MR1281754 (95g:52033)]}",
journal = j-MATH-INTEL,
volume = "17",
number = "1",
pages = "35--42",
year = "1995",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF03024716",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "52C17",
MRnumber = "1319992 (97f:52029)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Zong:1996:KNT,
author = "Chuanming Zong",
title = "The kissing numbers of tetrahedra",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "15",
number = "3",
pages = "251--264",
month = mar,
year = "1996",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/BF02711493",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "11H31 (52C07 52C17)",
MRnumber = "1380392 (97c:11070)",
MRreviewer = "Peter M. Gruber",
bibdate = "Wed Jan 09 10:08:13 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Book{Zong:1996:SPC,
editor = "Chuanming Zong and James Joseph Dudziak",
title = "Strange phenomena in convex and discrete geometry",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 158",
year = "1996",
DOI = "https://doi.org/10.1007/978-1-4613-8481-6",
ISBN = "0-387-94734-5 (softcover)",
ISBN-13 = "978-0-387-94734-1 (softcover)",
LCCN = "QA639.5 .Z66 1996",
MRclass = "52-01 (52-02)",
MRnumber = "1416567 (97m:52001)",
MRreviewer = "Peter M. Gruber",
bibdate = "Wed Jan 9 09:28:14 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Universitext",
acknowledgement = ack-nhfb,
subject = "Convex geometry; Discrete geometry",
}
@Article{Anonymous:1997:EDF,
author = "Anonymous",
title = "Erratum: {``The dimensional family approach in
(hyper)sphere packing: a typological study for new
patterns, structures, and interdimensional
functions''}",
journal = j-APPL-MATH-COMP,
volume = "88",
number = "1",
pages = "??--??",
day = "15",
month = dec,
year = "1997",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(97)00402-5",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:02:58 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.sciencedirect.com/science/journal/00963003",
note = "See \cite{Muses:1997:DFA,Muses:1998:EDF}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300397004025",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Bezdek:1997:IID,
author = "K{\'a}roly Bezdek",
title = "Isoperimetric inequalities and the dodecahedral
conjecture",
journal = j-INT-J-MATH,
volume = "8",
number = "6",
pages = "759--780",
year = "1997",
DOI = "https://doi.org/10.1142/S0129167X9700038X",
ISSN = "0129-167X",
MRclass = "52C17 (05B40 52B60)",
MRnumber = "1470853 (98k:52043)",
MRreviewer = "Salvatore Vassallo",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:1997:SPa,
author = "Thomas C. Hales",
title = "Sphere Packings, {I}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "17",
number = "1",
pages = "1--51",
month = jan,
year = "1997",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/BF02770863",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "1418278 (97k:52025)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg17.html#Hales97a;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/journals/00454/bibs/17n1p1.html",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:1997:SPb,
author = "Thomas C. Hales",
title = "Sphere Packings, {II}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "18",
number = "2",
pages = "135--149",
month = sep,
year = "1997",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/PL00009312",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "1455511 (98h:52033)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu Aug 13 17:55:00 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg18.html#Hales97;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/journals/00454/bibs/18n2p125.html",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Hales:1997:SPI,
author = "T. C. Hales",
title = "Sphere packings. {II}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "18",
number = "2",
pages = "135--149",
year = "1997",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/PL00009312",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "1455511 (98h:52033)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@InCollection{Leppmeier:1997:KWT,
author = "Max Leppmeier",
booktitle = "{{\"U}berblicke Mathematik 1996/97}. ({German})
[{Views} of Mathematics 1996/97]",
title = "{Kugelpackungen und Wurstkatastrophen oder Zur Theorie
der finiten und infiniten Packungen}. ({German})
[{Sphere packings and sausage} disasters or {On} the
theory of finite and infinite packings]",
publisher = pub-VIEWEG,
address = pub-VIEWEG:adr,
pages = "96--110",
year = "1997",
MRclass = "52C07 (52C17)",
MRnumber = "1644722 (99i:52018)",
MRreviewer = "Konrad J. Swanepoel",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "{\"U}berbl. Math.",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
language = "German",
}
@Article{Muses:1997:DFA,
author = "C. Mus{\`e}s",
title = "The dimensional family approach in (hyper)sphere
packing: a typological study of new patterns,
structures, and interdimensional functions",
journal = j-APPL-MATH-COMP,
volume = "88",
number = "1",
pages = "1--26",
day = "15",
month = dec,
year = "1997",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(97)00004-0",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:02:58 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.sciencedirect.com/science/journal/00963003",
note = "See errata \cite{Anonymous:1997:EDF,Muses:1998:EDF}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300397000040",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Betke:1998:FPS,
author = "Ulrich Betke and Martin Henk",
title = "Finite Packings of Spheres",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "19",
number = "2",
pages = "197--227",
month = feb,
year = "1998",
CODEN = "DCGEER",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg19.html#BetkeH98;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/journals/00454/bibs/19n2p197.html",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Bezdek:1998:FUS,
author = "Andr{\'a}s Bezdek and K{\'a}roly Bezdek and Robert
Connelly",
title = "Finite and Uniform Stability of Sphere Packings",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "20",
number = "1",
pages = "111--130",
month = jul,
year = "1998",
CODEN = "DCGEER",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg20.html#BezdekBC98;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/journals/00454/bibs/20n1p111.html",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Unpublished{Hales:1998:KC,
author = "T. Hales",
title = "The {Kepler Conjecture}",
year = "1998",
bibdate = "Thu Aug 13 16:43:12 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "arXiv:math.MG/9811078",
acknowledgement = ack-nhfb,
}
@Article{Henk:1998:KIC,
author = "Martin Henk",
title = "{Kugeln im Computer: ein Beweis der Keplerschen
Vermutung?}. ({German}) [{Spheres} in the computer: a
proof of {Kepler}'s Conjecture?]",
journal = j-MDMV,
volume = "??",
number = "4",
pages = "58--60",
year = "1998",
CODEN = "????",
ISSN = "0947-4471",
MRclass = "52C17",
MRnumber = "1666722",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Mitteilungen der Deutschen Mathematiker-Vereinigung",
keywords = "Kepler sphere-packing conjecture",
language = "German",
}
@Article{Muses:1998:EDF,
author = "C. Mus{\`e}s",
title = "Erratum: {``The dimensional family approach in
(hyper)sphere packing: a typological study for new
patterns, structures, and interdimensional functions'':
Appl. Math. Comput. {\bf 88} (1997)}",
journal = j-APPL-MATH-COMP,
volume = "97",
number = "2--3",
pages = "295--295",
day = "15",
month = dec,
year = "1998",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(98)00030-7",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:03:17 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.sciencedirect.com/science/journal/00963003",
note = "See \cite{Muses:1997:DFA,Anonymous:1997:EDF}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300398000307",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Rintoul:1998:HSS,
author = "M. D. Rintoul and S. S. Torquato",
title = "Hard-sphere statistics along the metastable amorphous
branch",
journal = j-PHYS-REV-E,
volume = "58",
number = "??",
pages = "532--537",
month = "????",
year = "1998",
CODEN = "PLEEE8",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Fri Aug 14 21:36:55 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Anonymous:1999:ICH,
author = "Anonymous",
title = "Interval Computations Help in Proving the {Kepler}
Conjecture",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "2",
pages = "197--199",
month = may,
year = "1999",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1017205323815",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 16:00:57 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=5&issue=2;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1017205323815/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=5&issue=2&spage=197-199",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Blinovsky:1999:MPE,
author = "Volodia Blinovsky",
title = "Multiple Packing of the {Euclidean} Sphere",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "45",
number = "4",
pages = "1334--1337",
month = apr,
year = "1999",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.761296",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/tit/tit45.html#Blinovsky99;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
}
@Article{Stephenson:1999:SSD,
author = "Paul Stephenson",
title = "Solitary Solarians and Densely Packed Spheres: From
{Stephen Hales} to {Thomas Hales}",
journal = j-MATH-GAZ,
volume = "83",
number = "498",
pages = "426--432",
month = nov,
year = "1999",
CODEN = "MAGAAS",
ISSN = "0025-5572",
bibdate = "Thu Aug 13 16:36:51 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.jstor.org/stable/3620952",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Talata:1999:TKN,
author = "Istv{\'a}n Talata",
title = "The translative kissing number of tetrahedra is $ 18
$",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "22",
number = "2",
pages = "231--248",
month = sep,
year = "1999",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/PL00009457",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "1698544 (2000e:52021)",
bibdate = "Wed Jan 09 09:59:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Toth:1999:MCP,
author = "L. Fejes T{\'o}th",
title = "{Minkowski} Circle Packings on the Sphere",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "22",
number = "2",
pages = "161--166",
month = sep,
year = "1999",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/PL00009451",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C15",
MRnumber = "1698538 (2000e:52018)",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg22.html#Toth99;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/journals/00454/bibs/22n2p161.html",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Wang:1999:PUS,
author = "Jie Wang",
title = "Packing of Unequal Spheres and Automated Radiosurgical
Treatment Planning",
journal = j-J-COMB-OPTIM,
volume = "3",
number = "4",
pages = "453--463",
year = "1999",
CODEN = "JCOPFV",
ISSN = "1382-6905",
ISSN-L = "1382-6905",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/jco/jco3.html#Wang99;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Optimization",
}
@Article{Weaire:1999:SHP,
author = "D. Weaire",
title = "A short history of packing problems",
journal = j-FORMA,
volume = "14",
number = "4",
pages = "279--285",
year = "1999",
ISSN = "0911-6036",
MRclass = "01A05 (52-03 52C17)",
MRnumber = "1770214 (2001e:01005)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Proceedings of the 2nd International Katachi U
Symmetry Symposium, Part 1 (Tsukuba, 1999).",
acknowledgement = ack-nhfb,
fjournal = "Forma",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Zhang:1999:OPP,
author = "J. Zhang and R. Blaak and E. Trizac and J. A. Cuesta
and D. Frenkel",
title = "Optimal packing of polydisperse hard-sphere fluids",
journal = j-J-CHEM-PHYS,
volume = "110",
number = "11",
pages = "5318--5324",
year = "1999",
CODEN = "JCPSA6",
ISSN = "0021-9606 (print), 1089-7690 (electronic)",
ISSN-L = "0021-9606",
bibdate = "Fri Aug 14 17:30:31 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Chemical Physics",
journal-URL = "http://scitation.aip.org/content/aip/journal/jcp/browse",
}
@Book{Zong:1999:SP,
author = "Chuanming Zong and J. (John) Talbot",
title = "Sphere packings",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 241",
year = "1999",
ISBN = "0-387-98794-0",
ISBN-13 = "978-0-387-98794-1",
LCCN = "QA166.7 .Z66 1999",
MRclass = "52C22 (11H31)",
MRnumber = "1707318 (2000g:52020)",
MRreviewer = "Peter M. Gruber",
bibdate = "Thu Aug 13 16:26:48 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Universitext",
URL = "http://www.loc.gov/catdir/enhancements/fy0816/99015367-d.html;
http://www.loc.gov/catdir/enhancements/fy0816/99015367-t.html",
acknowledgement = ack-nhfb,
subject = "sphere packings",
}
@Book{Aste:2000:PPP,
author = "Tomaso Aste and Denis Weaire",
title = "The Pursuit of Perfect Packing",
publisher = pub-IOP,
address = pub-IOP:adr,
pages = "xi + 136",
year = "2000",
DOI = "https://doi.org/10.1887/0750306483",
ISBN = "0-7503-0647-5 (hardcover), 0-7503-0648-3 (paperback)",
ISBN-13 = "978-0-7503-0647-8 (hardcover), 978-0-7503-0648-5
(paperback)",
LCCN = "QA166.7 .A78 2000",
MRclass = "52-01 (52A40 52C15 52C17 52C23)",
MRnumber = "1786410 (2001g:52001)",
MRreviewer = "Johann Linhart",
bibdate = "Tue Mar 13 11:03:37 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
abstract = "\booktitle{The Pursuit of Perfect Packing} explores
the densest possible arrangement of identical spheres
and many others problems that have to do with packing
things together. The examples from mathematics,
physics, biology, and engineering include the
arrangement of soap bubbles in foam, atoms in a
crystal, the architecture of the bee's honeycomb, and
the structure of the Giant's Causeway. The book also
contains brief accounts of the lives of many of the
scientists who devoted themselves to problems of
packing over many centuries, together with wry comments
on their efforts. It is an entertaining introduction to
the field for both specialists and the more general
public.",
acknowledgement = ack-nhfb,
keywords = "Hilbert's 18th Problem (How can one arrange most
densely in space an infinite number of equal solids of
given form, so that the ratio of the filled to the
unfilled space may be as great as possible?); Kepler
sphere-packing conjecture; Malfatti problem; Mallet's
model; Thomas Hales' packing-proof programme; Thomson
problem; Tammes problem; Vorono{\"\i} construction",
libnote = "Not in my library.",
remark = "This is an interesting little monograph on packing
problems, a surprising number of which continue to
elude proofs and solutions. Packing problems are
considered in two-, three-, and higher dimensions, for
bubbles, casks of Guinness, concrete, spheres, foam,
soap film, \ldots{}.",
tableofcontents = "1: How many sweets in the jar? \\
2: Loose change and tight packing \\
3: Hard Problems with hard spheres \\
4: Proof positive? \\
5: Peas and Pips \\
6: Enthusiastic admiration: the honeycomb \\
7: Toils and troubles with bubbles \\
8: The architecture of the world of atoms \\
9: Apollonius and concrete \\
10: The Giants Causeway \\
11: Soccer balls, golf balls, and Bucky balls \\
12: Packings and kisses in high dimensions \\
13: Odds and ends \\
14: Conclusion",
}
@TechReport{Barg:2000:BPS,
author = "A. Barg and D. Nogin",
title = "Bounds for Packings of Spheres in the {Grassmann}
Manifolds",
number = "2000-19",
institution = "DIMACS",
month = jul # " 27",
year = "2000",
bibdate = "Fri Aug 14 17:30:34 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Sat, 5 Aug 2000 13:00:00 GMT",
URL = "ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-19.ps.gz",
abstract = "We derive the Varshamov--Gilbert and Hamming bounds
for packings of spheres (codes) in the Grassmann
manifolds over $ \mathbb R $ and $ \mathbb C $. The
distance between two $k$-planes is defined as $ \rho
(p, q) = (\sin^2 \theta_1 + \dots + \sin^2 \theta_k)^{1
/ 2}$, where $ \theta_i, 1 \le i \le k$, are the
principal angles between $p$ and $q$.",
acknowledgement = ack-nhfb,
}
@Article{Betke:2000:DLP,
author = "U. Betke and M. Henk",
title = "Densest lattice packings of 3-polytopes",
journal = j-COMP-GEOM,
volume = "16",
number = "3",
pages = "157--186",
month = jul,
year = "2000",
DOI = "https://doi.org/10.1016/S0925-7721(00)00007-9",
ISSN = "0925-7721",
ISSN-L = "0925-7721",
bibdate = "Fri Aug 14 17:12:07 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
abstract = "Based on Minkowski's work on critical lattices of
3-dimensional convex bodies we present an efficient
algorithm for computing the density of a densest
lattice packing of an arbitrary 3-polytope. As an
application we calculate densest lattice packings of
all regular and Archimedean polytopes.",
acknowledgement = ack-nhfb,
fjournal = "Computational Geometry. Theory and Applications",
}
@Article{Cicalese:2000:OCO,
author = "Ferdinando Cicalese and Daniele Mundici",
title = "Optimal Coding with One Asymmetric Error: Below the
Sphere Packing Bound",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1858",
pages = "159--??",
year = "2000",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Feb 1 09:16:48 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1858.htm;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1858/18580159.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1858/18580159.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Hales:2000:ARM,
author = "T. C. Hales and P. Sarnak and M. C. Pugh",
title = "Advances in Random Matrix Theory, Zeta Functions, and
Sphere Packing",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "97",
number = "24",
pages = "12963--12964",
day = "21",
month = nov,
year = "2000",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.220396097",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
MRclass = "11H31 (11M26 52C17)",
MRnumber = "1795618 (2001k:11121)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.jstor.org/stable/123637",
abstract = "Over four hundred years ago, Sir Walter Raleigh asked
his mathematical assistant to find formulas for the
number of cannonballs in regularly stacked piles. These
investigations aroused the curiosity of the astronomer
Johannes Kepler and led to a problem that has gone
centuries without a solution: why is the familiar
cannonball stack the most efficient arrangement
possible? Here we discuss the solution that Hales found
in 1998. Almost every part of the 282-page proof relies
on long computer verifications. Random matrix theory
was developed by physicists to describe the spectra of
complex nuclei. In particular, the statistical
fluctuations of the eigenvalues (``the energy levels'')
follow certain universal laws based on symmetry types.
We describe these and then discuss the remarkable
appearance of these laws for zeros of the Riemann zeta
function (which is the generating function for prime
numbers and is the last special function from the last
century that is not understood today.) Explaining this
phenomenon is a central problem. These topics are
distinct, so we present them separately with their own
introductory remarks.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:2000:CH,
author = "Thomas C. Hales",
title = "Cannonballs and Honeycombs",
journal = j-NAMS,
volume = "47",
number = "4",
pages = "440--449",
month = apr,
year = "2000",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "52C17 (52C20 52C22)",
MRnumber = "1745624 (2000m:52027)",
MRreviewer = "R. Blind",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "In January 2003, the author was awarded the Chauvenet
Prize of the Mathematical Association of America for
this article.",
URL = "http://www.ams.org/notices/200004/fea-hales.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
keywords = "Kepler sphere-packing conjecture",
}
@InCollection{Henk:2000:KIC,
author = "Martin Henk and G{\"u}nter M. Ziegler",
booktitle = "Alles {Mathematik}. ({German}) [{All} mathematics]",
title = "{Kugeln im Computer---die Kepler-Vermutung}.
({German}) [{Spheres} in the computer --- the {Kepler}
conjecture]",
publisher = pub-VIEWEG,
address = pub-VIEWEG:adr,
pages = "121--143",
year = "2000",
MRclass = "52C17",
MRnumber = "1801830",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
language = "German",
}
@Article{Hilbert:2000:MP,
author = "David Hilbert",
title = "Mathematical problems",
journal = j-BULL-AMS,
volume = "37",
number = "4",
pages = "407--436",
month = "????",
year = "2000",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0273-0979-00-00881-8",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRclass = "01A75",
MRnumber = "1779412",
bibdate = "Wed Jan 09 17:19:41 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Lecture delivered before the International Congress of
Mathematicians at Paris in 1900. Reprint of
\cite{Hilbert:1902:MP}. English translation of
\cite{Hilbert:1900:MPV, Hilbert:1901:MPV}.",
URL = "http://www.ams.org/journals/bull/2000-37-04/S0273-0979-00-00881-8/S0273-0979-00-00881-8.pdf",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
keywords = "Hilbert's 23 Problems",
}
@Article{Klarreich:2000:FH,
author = "Erica G. Klarreich",
title = "Foams and honeycombs",
journal = j-AM-SCI,
volume = "88",
number = "2",
pages = "150--161",
month = mar # "\slash " # apr,
year = "2000",
CODEN = "AMSCAC",
DOI = "https://doi.org/10.1511/2000.2.152",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Wed Jan 09 15:14:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.americanscientist.org/issues/feature/2000/2/foams-and-honeycombs",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
remark = "Morgan writes \cite{Morgan:2005:BRB}, ``So despite
similarities, Kepler s Conjecture on sphere packing in
$ \mathbb {R}^3 $ was orders of magnitude more
difficult than the Hexagonal Honeycomb Conjecture in $
\mathbb {R}^2 $, mainly because $ \mathbb {R}^3 $
provides so many more geometric possibilities than $
\mathbb {R}^2 $. But it was easier in one aspect: it is
a packing problem, whereas the Honeycomb Conjecture is
a partitioning problem. The optimal two-dimensional
packing, with six circles fitting perfectly around
every circle, is relatively easy and was proved in 1890
by Thue. (See Klarreich [this paper] for a beautiful
account.)",
}
@Article{Li:2000:BAF,
author = "X.-Y. Li and S.-H. Teng and A. {\"U}ng{\"o}r",
title = "Biting: advancing front meets sphere packing",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "49",
number = "1-2",
pages = "61--81",
year = "2000",
CODEN = "IJNMBH",
ISSN = "0029-5981",
ISSN-L = "0029-5981",
bibdate = "Thu Aug 13 17:45:47 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
}
@Article{Muses:2000:VKC,
author = "C. Mus{\`e}s",
title = "Validating {Kepler's Conjecture}: a new approach",
journal = j-APPL-MATH-COMP,
volume = "110",
number = "1",
pages = "99--104",
year = "2000",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(99)00058-2",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "52C17",
MRnumber = "1743359",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.elsevier.com/locate/issn/00963003;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.elsevier.nl/gej-ng/29/17/20/83/21/24/abstract.html;
http://www.elsevier.nl/gej-ng/29/17/20/83/21/24/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Oesterle:2000:DME,
author = "Joseph Oesterl{\'e}",
title = "Densit{\'e} maximale des empilements de sph{\`e}res en
dimension 3 (d'apr{\`e}s {Thomas C. Hales} et {Samuel
P. Ferguson}). ({French}) [Maximal 3-dimensional
sphere-packing density (according to {Thomas C. Hales}
et {Samuel P. Ferguson})]",
journal = "Ast{\'e}risque",
volume = "266",
number = "863(5)",
pages = "405--413",
year = "2000",
ISSN = "0303-1179",
MRclass = "52C17 (52A40)",
MRnumber = "1772681 (2001k:52030)",
MRreviewer = "A. Florian",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "S{\'e}minaire Bourbaki, Vol. 1998/99. Exp. no. 863,
5.",
acknowledgement = ack-nhfb,
fjournal = "Ast\'erisque",
keywords = "Kepler sphere-packing conjecture",
language = "French",
}
@Article{Schnell:2000:FVH,
author = "Uwe Schnell",
title = "{FCC} versus {HCP} via parametric density",
journal = j-DISCRETE-MATH,
volume = "211",
number = "1-3",
pages = "269--274",
year = "2000",
CODEN = "DSMHA4",
DOI = "https://doi.org/10.1016/S0012-365X(99)00158-2",
ISSN = "0012-365X",
ISSN-L = "0012-365X",
MRclass = "52C17 (52C23)",
MRnumber = "1735333 (2001f:52040)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete Mathematics",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Wang:2000:MAO,
author = "Jie Wang",
title = "Medial Axis and Optimal Locations for Min-Max Sphere
Packing",
journal = j-J-COMB-OPTIM,
volume = "4",
number = "4",
pages = "487--503",
year = "2000",
CODEN = "JCOPFV",
ISSN = "1382-6905",
ISSN-L = "1382-6905",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/jco/jco4.html#Wang00;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Optimization",
}
@InProceedings{Backofen:2001:OCF,
author = "Rolf Backofen and Sebastian Will",
title = "Optimally Compact Finite Sphere Packings ---
Hydrophobic Cores in the {FCC}",
crossref = "Amir:2001:CPM",
volume = "2089",
pages = "257--272",
year = "2001",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/cpm/cpm2001.html#BackofenW01;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2089/20890257.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2089/20890257.pdf;
http://link.springer-ny.com/link/service/series/0558/tocs/t2089.htm",
acknowledgement = ack-nhfb,
}
@Book{Casti:2001:MMF,
author = "J. L. Casti",
title = "Mathematical mountaintops: the five most famous
problems of all time",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "177 + 3",
year = "2001",
ISBN = "0-19-514171-7",
ISBN-13 = "978-0-19-514171-9",
LCCN = "QA93 .C386 2001",
bibdate = "Wed Jan 9 08:09:14 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Mathematics; Popular works",
tableofcontents = "The art of the problem \\
Hilbert's tenth problem \\
The four-color problem \\
The continuum hypothesis \\
The Kepler conjecture \\
Fermat's last theorem \\
The magnificent seven",
}
@InProceedings{Chen:2001:ACS,
author = "Danny Z. Chen and Xiaobo Hu and Yingping Huang and
Yifan Li and Jinhui Xu",
title = "Algorithms for congruent sphere packing and
applications",
crossref = "ACM:2001:PSA",
pages = "212--221",
year = "2001",
DOI = "https://doi.org/10.1145/378583.378672",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/compgeom/compgeom2001.html#ChenHHLX01;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Book{Cornuejols:2001:COP,
author = "G{\'e}rard Cornu{\'e}jols",
title = "Combinatorial Optimization: Packing and Covering",
volume = "74",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xi + 132",
year = "2001",
DOI = "https://doi.org/10.1137/1.9780898717105",
ISBN = "0-89871-481-8 (paperback)",
ISBN-13 = "978-0-89871-481-4 (paperback)",
LCCN = "QA166.7 .C67 2001",
MRclass = "90-02 (05-02 52C17 52C45 90C27 90C35)",
MRnumber = "1828452 (2002e:90004)",
MRreviewer = "Rainer Burkard",
bibdate = "Wed Jan 9 09:48:56 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "CBMS-NSF regional conference series in applied
mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0708/00066073-d.html;
http://www.loc.gov/catdir/enhancements/fy0708/00066073-t.html",
acknowledgement = ack-nhfb,
subject = "Combinatorial packing and covering",
}
@InCollection{Gardner:2001:PS,
author = "Martin Gardner",
title = "Packing spheres",
crossref = "Gardner:2001:CBM",
chapter = "10",
pages = "128--136",
year = "2001",
bibdate = "Wed Jan 09 17:54:03 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Page 135 mentions a conjecture by Stan Ulam in 1972
that ``the maximal density ($ \approx 0.74048$) for
packing congruent spheres is smaller than that for any
other convex body'' \cite[page
1547]{Lagarias:2012:MPR}.",
acknowledgement = ack-nhfb,
}
@Article{Hales:2001:HC,
author = "Thomas C. Hales",
title = "The honeycomb conjecture",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "25",
number = "1",
pages = "1--22",
month = jan,
year = "2001",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s004540010071",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C20 (51M16)",
MRnumber = "1797293 (2002a:52020)",
MRreviewer = "W. Kuperberg",
bibdate = "Wed Jan 09 15:18:38 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@InProceedings{Hales:2001:SPG,
author = "Thomas C. Hales",
title = "Sphere packings and generative [{XXX}?]",
crossref = "ACM:2001:PSA",
pages = "69--69",
year = "2001",
DOI = "https://doi.org/10.1145/378583.378624",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/compgeom/compgeom2001.html#Hales01;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Book{Hsiang:2001:LAP,
author = "Wu Yi Hsiang",
title = "Least action principle of crystal formation of dense
packing type and {Kepler}'s conjecture",
volume = "3",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xxii + 402",
year = "2001",
DOI = "https://doi.org/10.1142/9789812384911",
ISBN = "981-02-4670-6",
ISBN-13 = "978-981-02-4670-9",
LCCN = "QA166.7 .H85 2001",
MRclass = "52C17",
MRnumber = "1962807 (2004g:52033)",
MRreviewer = "Udo Hertrich-Jeromin",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
note = "With a foreword by S. S. Chern",
series = "Nankai Tracts in Mathematics",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
subject = "Kepler's conjecture; Sphere packings; Crystallography,
Mathematical",
xxpages = "xxi + 402",
}
@Article{Torquato:2001:MGS,
author = "S. Torquato and F. H. Stillinger",
title = "Multiplicity of generation, selection, and
classification procedures for jammed hard-particle
packings",
journal = j-J-PHYS-CHEM-B,
volume = "105",
number = "47",
pages = "11849--11853",
day = "13",
month = oct,
year = "2001",
CODEN = "JPCBFK",
DOI = "https://doi.org/10.1021/jp011960q",
ISSN = "1089-5647 (print), 1520-6106 (electronic)",
ISSN-L = "1520-5207",
bibdate = "Fri Aug 14 21:41:30 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physical Chemistry. B. Condensed matter,
materials, surfaces, interfaces \& biophysical",
journal-URL = "http://pubs.acs.org/loi/jpcbfk",
}
@InCollection{Verger-Gaugry:2001:RSP,
author = "Jean-Louis Verger-Gaugry",
booktitle = "{S{\'e}minaire de Th{\'e}orie Spectrale et
G{\'e}om{\'e}trie, Vol. 19, Ann{\'e}e 2000--2001}",
title = "Remarks on sphere packings, clusters and {Hales}
{Ferguson} theorem",
volume = "19",
publisher = "Universit{\'e} Grenoble I",
address = "Saint-Martin-d'H{\`e}res, France",
pages = "165--177",
year = "2001",
MRclass = "52C17 (52C23)",
MRnumber = "1909081 (2003d:52021)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "S{\'e}min. Th{\'e}or. Spectr. G{\'e}om.",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Barg:2002:BPS,
author = "Alexander Barg and Dmitry Yu. Nogin",
title = "Bounds on packings of spheres in the {Grassmann}
manifold",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "48",
number = "9",
pages = "2450--2454",
month = sep,
year = "2002",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/TIT.2002.801469",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/tit/tit48.html#BargN02;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
}
@InProceedings{Cornforth:2002:EOB,
author = "David Cornforth",
title = "Evolution in the Orange Box --- {A} New Approach to
the Sphere-Packing Problem in {CMAC}-Based Neural
Networks",
crossref = "McKay:2002:AAA",
pages = "333--343",
year = "2002",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/ausai/ausai2002.html#Cornforth02;
http://link.springer-ny.com/link/service/series/0558/tocs/t2557.htm;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/series/0558/bibs/2557/25570333.htm;
http://link.springer.de/link/service/series/0558/papers/2557/25570333.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Gervois:2002:VRT,
author = "A. Gervois and Luc Oger and Patrick Richard and Jean
Paul Troadec",
title = "{Voronoi} and Radical Tessellations of Packings of
Spheres",
crossref = "Sloot:2002:CSIc",
volume = "2331",
pages = "95--104",
year = "2002",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/iccS/iccS2002-3.html#GervoisORT02;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/series/0558/bibs/2331/23310095.htm",
acknowledgement = ack-nhfb,
}
@InProceedings{Hales:2002:CVK,
author = "Thomas C. Hales",
booktitle = "{Proceedings of the International Congress of
Mathematicians, Vol. III (Beijing, 2002)}",
title = "A computer verification of the {Kepler Conjecture}",
publisher = "Higher Education Press",
address = "Beijing, People's Republic of China",
pages = "795--804",
year = "2002",
MRclass = "52C17",
MRnumber = "1957580 (2004a:52036)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Lagarias:2002:BLD,
author = "J. C. Lagarias",
title = "Bounds for local density of sphere packings and the
{Kepler Conjecture}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "27",
number = "2",
pages = "165--193",
month = jan,
year = "2002",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/978-1-4614-1129-1_2",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "1880936 (2002k:52027)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/journals/00454/contents/01/0060/",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@InProceedings{March:2002:EVF,
author = "N. H. March and M. P. Tosi",
title = "Excluded Volume, Free Volume and Hard Sphere Packing",
crossref = "March:2002:ILS",
pages = "29--50",
year = "2002",
DOI = "https://doi.org/10.1142/9789812778482_0002",
bibdate = "Fri May 31 08:35:00 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/march-norman-h.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.worldscientific.com/doi/abs/10.1142/9789812778482_0002",
acknowledgement = ack-nhfb,
book-URL = "http://www.worldscientific.com/worldscibooks/10.1142/4717",
}
@Article{Molnar:2002:BTO,
author = "E. Moln{\'a}r and I. Prok and J. Szirmai",
title = "{Bestimmung der transitiven optimalen Kugelpackungen
f{\"u}r die 29 Raumgruppen, die Coxetersche
Spiegelungsuntergruppen enthalten}. ({German})
[{Characterization} of transitive optimal sphere
packings for the 29 space groups containing {Coxeter}
reflection subgroups]",
journal = "Studia Sci. Math. Hungar.",
volume = "39",
number = "3-4",
pages = "443--483",
year = "2002",
CODEN = "SSMHAX",
DOI = "https://doi.org/10.1556/SScMath.39.2002.3-4.13",
ISSN = "0081-6906",
MRclass = "52C17 (20H15 52A40 52B10)",
MRnumber = "1956950 (2004a:52038)",
bibdate = "Thu Apr 12 18:15:18 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Studia Scientiarum Mathematicarum Hungarica. A
Quarterly of the Hungarian Academy of Sciences",
language = "German",
}
@Article{Bowen:2003:DPE,
author = "Lewis Bowen and Charles Radin",
title = "Densest Packing of Equal Spheres in Hyperbolic Space",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "29",
number = "1",
pages = "23--39",
month = dec,
year = "2003",
CODEN = "DCGEER",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg29.html#BowenR03;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.de/link/service/journals/00454/contents/02/2791/index.html",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Cohn:2003:NUB,
author = "Henry Cohn and Noam Elkies",
title = "New Upper Bounds on Sphere Packings {I}",
journal = j-ANN-MATH-2,
volume = "157",
number = "2",
pages = "698--714",
month = mar,
year = "2003",
CODEN = "ANMAAH",
ISSN = "0003-486X (print), 1939-8980 (electronic)",
ISSN-L = "0003-486X",
bibdate = "Thu Aug 13 16:38:01 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.jstor.org/stable/3597215",
abstract = "We develop an analogue for sphere packing of the
linear programming bounds for error-correcting codes,
and use it to prove upper bounds for the density of
sphere packings, which are the best bounds known at
least for dimensions 4 through 36. We conjecture that
our approach can be used to solve the sphere packing
problem in dimensions 8 and 24.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics (2)",
journal-URL = "http://www.jstor.org/action/showPublication?journalCode=annamath",
}
@Article{Cox:2003:MPI,
author = "S. J. Cox and F. Graner and M. Fatima Vaz and C.
Monnereaupittet and N. Pittet",
title = "Minimal perimeter for {$N$} identical bubbles in two
dimensions: calculations and simulations",
journal = j-PHIL-MAGAZINE,
volume = "83",
number = "??",
pages = "1393--1406",
month = "????",
year = "2003",
CODEN = "PHMAA4",
DOI = "",
ISSN = "0031-8086",
bibdate = "Wed Jan 09 15:22:36 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Magazine",
journal-URL = "http://www.tandfonline.com/loi/tphm19",
}
@InCollection{Hales:2003:SAA,
author = "Thomas C. Hales",
booktitle = "Discrete and computational geometry",
title = "Some algorithms arising in the proof of the {Kepler
Conjecture}",
volume = "25",
publisher = pub-SV,
address = pub-SV:adr,
pages = "489--507",
year = "2003",
DOI = "https://doi.org/10.1007/978-3-642-55566-4_22",
MRclass = "52C17 (90C27)",
MRnumber = "2038488 (2005b:52047)",
MRreviewer = "Achill Sch{\"u}rmann",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Algorithms Combin.",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hauser:2003:GPM,
author = "Kai Hauser and Reinhard Lang",
title = "On the geometrical and physical meaning of {Newton}'s
solution to {Kepler}'s problem",
journal = j-MATH-INTEL,
volume = "25",
number = "4",
pages = "35--44",
year = "2003",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF02984860",
ISSN = "0343-6993",
ISSN-L = "0343-6993",
MRclass = "70F05 (01A45 52C17 70-03)",
MRnumber = "2012561 (2005a:70009)",
MRreviewer = "Florin N. Diacu",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
keywords = "Kepler sphere-packing conjecture",
}
@Book{Szpiro:2003:KC,
author = "George G. Szpiro",
title = "{Kepler}'s conjecture",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "viii + 296",
year = "2003",
ISBN = "0-471-08601-0",
ISBN-13 = "978-0-471-08601-7",
MRclass = "52C17 (01A05 05B40 52-03)",
MRnumber = "2133723 (2007c:52023)",
MRreviewer = "P. D. F. Ion",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "How some of the greatest minds in history helped solve
one of the oldest math problems in the world",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Book{Szpiro:2003:KCH,
editor = "George Szpiro",
title = "{Kepler's Conjecture}: how some of the greatest minds
in history helped solve one of the oldest math problems
in the world",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "viii + 296",
year = "2003",
ISBN = "0-471-08601-0",
ISBN-13 = "978-0-471-08601-7",
LCCN = "QA93 .S97 2003",
MRclass = "52C17 (01A05 05B40 52-03)",
MRnumber = "2133723 (2007c:52023)",
MRreviewer = "P. D. F. Ion",
bibdate = "Thu Aug 13 16:25:44 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/wiley046/2002014422.html;
http://www.loc.gov/catdir/description/wiley039/2002014422.html;
http://www.loc.gov/catdir/toc/wiley031/2002014422.html",
acknowledgement = ack-nhfb,
subject = "Mathematics; Popular works",
tableofcontents = "Cannonballs and tomatoes \\
The puzzle of the dozen spheres \\
Fire hydrants and soccer players \\
Thue's two attempts and Fejes-T\'oth's achievement \\
Twelve's company, thirteen's a crowd \\
Nets and knots \\
Twisted boxes \\
No dancing at this congress \\
The race for the upper bound \\
Right angles for round spaces \\
Wobbly balls and hybrid stars \\
Simplex, Cplex, and symbolic mathematics \\
But is it really a proof? \\
Beehives again \ldots{} This is not an epilogue",
}
@Article{Szpiro:2003:MDP,
author = "George Szpiro",
title = "Mathematics: Does the proof stack up?",
journal = j-NATURE,
volume = "424",
number = "6944",
pages = "12--13",
day = "3",
month = jul,
year = "2003",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/424012a",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Jan 09 15:21:19 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.nature.com/nature/journal/v424/n6944/full/424012a.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "From the introduction: ``Think peer review takes too
long? One mathematician has waited four years to have
his paper refereed, only to hear that the exhausted
reviewers can't be certain whether his proof is
correct. George Szpiro investigates.''",
}
@Book{Boroczky:2004:FPC,
author = "K{\'a}roly {B{\"o}r{\"o}czky, Jr.}",
title = "Finite Packing and Covering",
volume = "154",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvii + 380",
year = "2004",
DOI = "https://doi.org/10.1017/CBO9780511546587",
ISBN = "0-521-80157-5",
ISBN-13 = "978-0-521-80157-7",
LCCN = "QA166.7 .B67 2004",
MRclass = "52C15 (05B40 52C17 52C20 52C22)",
MRnumber = "2078625 (2005g:52045)",
MRreviewer = "J. M. Wills",
bibdate = "Wed Jan 9 08:44:32 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Cambridge tracts in mathematics",
URL = "http://www.loc.gov/catdir/description/cam041/2003065450.html;
http://www.loc.gov/catdir/samples/cam051/2003065450.html;
http://www.loc.gov/catdir/toc/cam041/2003065450.html",
acknowledgement = ack-nhfb,
subject = "Combinatorial packing and covering",
}
@Article{Donev:2004:LPA,
author = "Aleksandar Donev and Salvatore Torquato and Frank H.
Stillinger and Robert Connelly",
title = "A linear programming algorithm to test for jamming in
hard-sphere packings",
journal = j-J-COMPUT-PHYS,
volume = "197",
number = "1",
pages = "139--166",
day = "10",
month = jun,
year = "2004",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2003.11.022",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:12:40 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999103006235",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Donev:2004:UDC,
author = "A. Donev and F. H. Stillinger and P. M. Chaikin and S.
Torquato",
title = "Unusually dense crystal ellipsoid packings",
journal = j-PHYS-REV-LET,
volume = "92",
number = "25",
pages = "255506",
day = "25",
month = jun,
year = "2004",
CODEN = "PRLTAO",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Fri Aug 14 21:29:02 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
pagecount = "4",
}
@Article{Gensane:2004:DPE,
author = "Thierry Gensane",
title = "Dense Packings of Equal Spheres in a Cube",
journal = j-ELECT-J-COMB,
volume = "11",
number = "1",
year = "2004",
ISSN = "1077-8926 (print), 1097-1440 (electronic)",
ISSN-L = "1077-8926",
bibdate = "Thu Aug 13 18:08:00 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/combinatorics/combinatorics11.html#Gensane04;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.combinatorics.org/Volume_11/Abstracts/v11i1r33.html",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Combinatorics",
}
@InProceedings{Hales:2004:FPK,
author = "Thomas C. Hales",
title = "Formalizing the Proof of the {Kepler Conjecture}",
crossref = "Slind:2004:TPH",
pages = "117--117",
year = "2004",
bibdate = "Thu Aug 13 17:33:59 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/tphol/tphol2004.html#Hales04;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://springerlink.metapress.com/openurl.asp?genre=article&issn=0302-9743&spage=117;volume=3223",
acknowledgement = ack-nhfb,
}
@Article{Radin:2004:OOS,
author = "Charles Radin",
title = "Orbits of Orbs: Sphere Packing Meets {Penrose}
Tilings",
journal = j-AMER-MATH-MONTHLY,
volume = "111",
number = "2",
pages = "137--149",
month = feb,
year = "2004",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Thu Aug 13 16:41:03 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.jstor.org/stable/4145214",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Barg:2005:CBP,
author = "Alexander Barg and Dmitry Yu. Nogin",
title = "Correction to ``Bounds on Packings of Spheres in the
{Grassmann} Manifold''",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "51",
number = "7",
pages = "2732--2732",
month = jul,
year = "2005",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/TIT.2005.850231",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/tit/tit51.html#BargN05;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
}
@Article{Busa:2005:AFP,
author = "J{\'a}n Busa and Jozef Dzurina and Edik Hayryan and
Shura Hayryan and Chin-Kun Hu and J{\'a}n Pl{\'a}vka
and Imrich Pokorn{\'y} and Jaroslav Skriv{\'a}nek and
Ming-Chya Wu",
title = "{ARVO}: {A} {Fortran} package for computing the
solvent accessible surface area and the excluded volume
of overlapping spheres via analytic equations",
journal = j-COMP-PHYS-COMM,
volume = "165",
number = "1",
pages = "59--96",
year = "2005",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2004.08.002",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/cphysics/cphysics165.html#BusaDHHHPPSW05;
http://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Davies:2005:WM,
author = "Brian Davies",
title = "Whither Mathematics?",
journal = j-NAMS,
volume = "52",
number = "11",
pages = "1350--1356",
month = dec,
year = "2005",
CODEN = "AMNOAN",
ISSN = "0002-9920",
bibdate = "Tue Nov 29 05:30:24 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.ams.org/notices/200511/comm-davies.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
keywords = "classification of finite simple groups;
computer-assisted proofs; consistency of Peano
arithmetic; four-color theorem; interval arithmetic;
Kepler sphere-packing conjecture; Monster group",
}
@Article{Donev:2005:NLCa,
author = "Aleksandar Donev and Salvatore Torquato and Frank H.
Stillinger",
title = "Neighbor list collision-driven molecular dynamics
simulation for nonspherical hard particles. {I}.
{Algorithmic} details",
journal = j-J-COMPUT-PHYS,
volume = "202",
number = "2",
pages = "737--764",
day = "20",
month = jan,
year = "2005",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2004.08.014",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:12:47 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999104003146",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Donev:2005:NLCb,
author = "Aleksandar Donev and Salvatore Torquato and Frank H.
Stillinger",
title = "Neighbor list collision-driven molecular dynamics
simulation for nonspherical hard particles. {II}.
{Applications} to ellipses and ellipsoids",
journal = j-J-COMPUT-PHYS,
volume = "202",
number = "2",
pages = "765--793",
day = "20",
month = jan,
year = "2005",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2004.08.025",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:12:47 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999104003948",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Hales:2005:PKC,
author = "Thomas C. Hales",
title = "A proof of the {Kepler Conjecture}",
journal = j-ANN-MATH-2,
volume = "162",
number = "3",
pages = "1065--1185",
year = "2005",
CODEN = "ANMAAH",
DOI = "https://doi.org/10.4007/annals.2005.162.1065",
ISSN = "0003-486X (print), 1939-8980 (electronic)",
ISSN-L = "0003-486X",
MRclass = "52C17",
MRnumber = "2179728 (2006g:52029)",
MRreviewer = "G{\'e}za T{\'o}th",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "This proof is so complex that twelve journal referees
were unable to verify it between its submission in 1998
and publication seven years later, so the editors
decided to publish the article with a disclaimer about
the lack of proof verification; see
\cite{Morgan:2005:BRB} for more on this paper, and the
associated book \cite{Szpiro:2003:KCH}.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics. Second Series",
journal-URL = "http://www.jstor.org/action/showPublication?journalCode=annamath",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Henkel:2005:SPB,
author = "O. Henkel",
title = "Sphere-packing bounds in the {Grassmann} and {Stiefel}
manifolds",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "51",
number = "10",
pages = "3445--3456",
month = oct,
year = "2005",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/TIT.2005.855594",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/tit/tit51.html#Henkel05;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
}
@Article{Morgan:2005:BRB,
author = "Frank Morgan",
title = "Book Review: {{\booktitle{Kepler's Conjecture}} and
Hales' Proof}",
journal = j-NAMS,
volume = "52",
number = "1",
pages = "44--47",
month = jan,
year = "2005",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Wed Jan 09 07:58:15 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Review of \cite{Szpiro:2003:KCH}.",
URL = "http://www.ams.org/notices/200501/rev-morgan.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
remark = "\booktitle{Kepler's Conjecture: How some of the
greatest minds in history helped solve one of the
oldest math problems in the world}, George G. Szpiro,
John Wiley \& Sons, Inc., 2003, \$24.95, ISBN
0-471-08601-0.",
}
@Article{Muraz:2005:LBD,
author = "G. Muraz and J.-L. Verger-Gaugry",
title = "On Lower Bounds of the Density of {Delone} Sets and
Holes in Sequences of Sphere Packings",
journal = j-EXP-MATH,
volume = "14",
number = "1",
pages = "47--57",
month = "????",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2005.10128908",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Mon Mar 5 15:33:58 MST 2012",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.tandfonline.com/toc/uexm20/14/1",
URL = "http://projecteuclid.org/euclid.em/1120145569",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "30 Jan 2011",
}
@InProceedings{Obua:2005:PBR,
author = "Steven {Obua}",
title = "Proving bounds for real linear programs in
{Isabelle\slash HOL}",
crossref = "Hurd:2005:TPH",
pages = "227--244",
year = "2005",
DOI = "https://doi.org/10.1007/11541868",
MRclass = "68T15 90C05",
bibdate = "Thu May 22 16:22:40 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
ZMnumber = "1152.68531",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
}
@Article{Ambrus:2006:NLB,
author = "G. Ambrus and F. Fodor",
title = "A new lower bound on the surface area of a {Voronoi}
polyhedron",
journal = j-PERIOD-MATH-HUNGAR,
volume = "53",
number = "1-2",
pages = "45--58",
year = "2006",
CODEN = "PMHGAW",
DOI = "https://doi.org/10.1007/s10998-006-0020-5",
ISSN = "0031-5303",
ISSN-L = "0031-5303",
MRclass = "52C17 (52A40)",
MRnumber = "2286459 (2007m:52023)",
MRreviewer = "Konrad J. Swanepoel",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Periodica Mathematica Hungarica. Journal of the
J\'anos Bolyai Mathematical Society",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Bezdek:2006:SPR,
author = "K{\'a}roly Bezdek",
title = "Sphere packings revisited",
journal = j-EUR-J-COMB,
volume = "27",
number = "6",
pages = "864--883",
year = "2006",
CODEN = "EJOCDI",
DOI = "https://doi.org/10.1016/j.ejc.2005.05.001",
ISSN = "0195-6698",
ISSN-L = "0195-6698",
MRclass = "52C17 (05B40)",
MRnumber = "2226423 (2007a:52021)",
MRreviewer = "Gy{\"o}rgy D{\'o}sa",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/ejc/ejc27.html#Bezdek06;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Combinatorics",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Bundy:2006:VMD,
author = "Alan Bundy",
title = "A Very Mathematical Dilemma",
journal = j-COMP-J,
volume = "49",
number = "4",
pages = "480--486",
month = jul,
year = "2006",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxl021",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Jun 23 11:56:45 MDT 2006",
bibsource = "http://comjnl.oxfordjournals.org/content/vol49/issue4/index.dtl;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/content/abstract/49/4/480;
http://comjnl.oxfordjournals.org/cgi/content/full/49/4/480;
http://comjnl.oxfordjournals.org/cgi/reprint/49/4/480",
abstract = "Mathematics is facing a dilemma at its heart: the
nature of mathematical proof. We have known since
Church and Turing independently showed that
mathematical provability was undecidable that there are
theorems whose shortest proofs are enormous. Within the
last half-century we have discovered practical examples
of such theorems: the classification of all finite
simple groups, the Four Colour Theorem and Kepler's
Conjecture. These theorems were only proved with the
aid of a computer. But computer proof is very
controversial, with many mathematicians refusing to
accept a proof that has not been thoroughly checked and
understood by a human. The choice seems to be between
either abandoning the investigation of theorems whose
only proofs are enormous or changing traditional
mathematical practice to include computer-aided proofs.
Or is there a way to make large computer proofs more
accessible to human mathematicians?",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Conway:2006:PTC,
author = "J. H. Conway and S. Torquato",
title = "Packing, Tiling, and Covering with Tetrahedra",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "103",
number = "28",
pages = "10612--10617",
day = "11",
month = jul,
year = "2006",
CODEN = "PNASA6",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Thu Aug 13 16:39:01 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.jstor.org/stable/30049550",
abstract = "It is well known that three-dimensional Euclidean
space cannot be tiled by regular tetrahedra. But how
well can we do? In this work, we give several
constructions that may answer the various senses of
this question. In so doing, we provide some solutions
to packing, tiling, and covering problems of
tetrahedra. Our results suggest that the regular
tetrahedron may not be able to pack as densely as the
sphere, which would contradict a conjecture of Ulam.
The regular tetrahedron might even be the convex body
having the smallest possible packing density.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Article{Ferguson:2006:SPV,
author = "Samuel P. Ferguson",
title = "Sphere packings. {V}. {Pentahedral} prisms",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "36",
number = "1",
pages = "167--204",
month = jul,
year = "2006",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-005-1214-y",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (05B40)",
MRnumber = "2229661 (2007d:52025)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg36.html#Ferguson06;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:2006:FKC,
author = "Thomas C. Hales and Samuel P. Ferguson",
title = "A formulation of the {Kepler Conjecture}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "36",
number = "1",
pages = "21--69",
month = jul,
year = "2006",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-005-1211-1",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (05B40)",
MRnumber = "2229658 (2007d:52022)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:2006:HOK,
author = "Thomas C. Hales",
title = "Historical overview of the {Kepler Conjecture}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "36",
number = "1",
pages = "5--20",
month = jul,
year = "2006",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-005-1210-2",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (05B40)",
MRnumber = "2229657 (2007d:52021)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:2006:SPIa,
author = "Thomas C. Hales",
title = "Sphere packings. {III}. {Extremal} cases",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "36",
number = "1",
pages = "71--110",
month = jul,
year = "2006",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-005-1212-0",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (05B40)",
MRnumber = "2229659 (2007d:52023)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg36.html#Hales06a;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:2006:SPIb,
author = "Thomas C. Hales",
title = "Sphere Packings. {IV}. {Detailed} Bounds",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "36",
number = "1",
pages = "111--166",
month = jul,
year = "2006",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-005-1213-z",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (05B40)",
MRnumber = "2229660 (2007d:52024)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg36.html#Hales06b;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:2006:SPV,
author = "Thomas C. Hales",
title = "Sphere packings. {VI}. {Tame} graphs and linear
programs",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "36",
number = "1",
pages = "205--265",
month = jul,
year = "2006",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-005-1215-x",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (05B40 90C08)",
MRnumber = "2229662 (2007d:52026)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg36.html#Hales06c;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@InCollection{Nipkow:2006:FTG,
author = "Tobias Nipkow and Gertrud Bauer and Paula Schultz",
booktitle = "Automated reasoning",
title = "Flyspeck. {I}. {Tame} graphs",
volume = "4130",
publisher = pub-SV,
address = pub-SV:adr,
pages = "21--35",
year = "2006",
DOI = "https://doi.org/10.1007/11814771_4",
MRclass = "Database Expansion Item",
MRnumber = "2354670",
bibdate = "Thu May 22 17:30:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Lecture Notes in Comput. Sci.",
acknowledgement = ack-nhfb,
}
@Article{Parisi:2006:APH,
author = "G. Parisi and F. Zamponi",
title = "Amorphous packings of hard spheres in large space
dimension",
journal = "Computing Research Repository (CoRR)",
volume = "abs/cond-mat/0601573",
year = "2006",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/corr/corr0601.html#abs-cond-mat-0601573;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "informal publication",
URL = "http://arxiv.org/abs/cond-mat/0601573",
acknowledgement = ack-nhfb,
}
@Article{Sahai:2006:HBS,
author = "Anant Sahai",
title = "How to beat the sphere-packing bound with feedback",
journal = "Computing Research Repository (CoRR)",
volume = "abs/cs/0610139",
year = "2006",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/corr/corr0610.html#abs-cs-0610139;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "informal publication",
URL = "http://arxiv.org/abs/cs/0610139",
acknowledgement = ack-nhfb,
}
@Article{Schurmann:2006:PSC,
author = "Achill Sch{\"u}rmann",
title = "On packing spheres into containers",
journal = j-DOC-MATH,
volume = "11",
pages = "393--406 (electronic)",
year = "2006",
ISSN = "1431-0635",
ISSN-L = "1431-0635",
MRclass = "52C17 (01A45 05B40)",
MRnumber = "2288074 (2007j:52020)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Documenta Mathematica",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Skoge:2006:PHH,
author = "Monica Skoge and Aleksandar Donev and Frank H.
Stillinger and Salvatore Torquato",
title = "Packing hyperspheres in high-dimensional {Euclidean}
spaces",
journal = j-PHYS-REV-E,
volume = "74",
number = "4",
pages = "041127",
month = oct,
year = "2006",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.74.041127",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Wed Feb 29 20:59:25 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.74.041127",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
pagecount = "11",
}
@Article{Torquato:2006:NCL,
author = "S. Torquato and F. H. Stillinger",
title = "New Conjectural Lower Bounds on the Optimal Density of
Sphere Packings",
journal = j-EXP-MATH,
volume = "15",
number = "3",
pages = "307--331",
month = "????",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2006.10128964",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Mon Mar 5 15:43:50 MST 2012",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.tandfonline.com/toc/uexm20/15/3",
URL = "http://projecteuclid.org/euclid.em/1175789761",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "30 Jan 2011",
xxauthor = "F. H. Stillinger and S. Torquato",
xxpages = "307--332",
}
@Article{Torquato:2006:RSA,
author = "S. Torquato and O. U. Uche and F. H. Stillinger",
title = "Random sequential addition of hard spheres in high
{Euclidean} dimensions",
journal = j-PHYS-REV-E,
volume = "74",
number = "6 (part 1)",
pages = "061308",
month = dec,
year = "2006",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.74.061308",
ISSN = "1539-3755",
ISSN-L = "1539-3755",
bibdate = "Fri Jun 7 07:03:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Toth:2006:GEF,
author = "G{\'a}bor Fejes Toth and Jeffrey C. Lagarias",
title = "Guest editors' foreword {[The Kepler Conjecture by
Thomas C. Hales, with Samuel P.\ Ferguson]}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "36",
number = "1",
pages = "1--3",
month = jul,
year = "2006",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-005-1209-8",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52-06 (52C17)",
MRnumber = "2229656",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture",
}
@Book{Zong:2006:CWC,
author = "Chuanming Zong",
title = "The Cube: a Window to Convex and Discrete Geometry",
volume = "168",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 174",
year = "2006",
DOI = "https://doi.org/10.1017/CBO9780511543173",
ISBN = "0-521-85535-7 (hardcover)",
ISBN-13 = "978-0-521-85535-8 (hardcover)",
LCCN = "QA639.5 .Z64 2006",
MRclass = "52B12 (05C99 52B05 52B70 94A08)",
MRnumber = "2221660 (2007a:52016)",
bibdate = "Wed Jan 9 09:28:14 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Cambridge tracts in mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0642/2006296040-d.html;
http://www.loc.gov/catdir/enhancements/fy0642/2006296040-t.html;
http://www.loc.gov/catdir/enhancements/fy0733/2006296040-b.html",
acknowledgement = ack-nhfb,
subject = "Convex geometry; Discrete geometry",
}
@InProceedings{Anikeenko:2007:RQR,
author = "Alexey V. Anikeenko and Nikolai N. Medvedev",
title = "The Role of Quasi-Regular Tetrahedra in Dense
Disordered Packings of Hard Spheres",
crossref = "IEEE:2007:ISV",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "130--134",
year = "2007",
DOI = "https://doi.org/10.1109/ISVD.2007.36",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/isvd/isvd2007.html#AnikeenkoM07;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Article{Donev:2007:UJP,
author = "A. Donev and R. Connelly and F. H. Stillinger and S.
Torquato",
title = "Underconstrained jammed packings of nonspherical hard
particles: ellipses and ellipsoids",
journal = j-PHYS-REV-E,
volume = "75",
number = "5",
pages = "051304",
month = "????",
year = "2007",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.75.051304",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Fri Aug 14 21:43:34 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.75.051304",
abstract = "Continuing on recent computational and experimental
work on jammed packings of hard ellipsoids [Donev et
al., Science 303, 990 (2004)] we consider jamming in
packings of smooth strictly convex nonspherical hard
particles. We explain why an isocounting conjecture,
which states that for large disordered jammed packings
the average contact number per particle is twice the
number of degrees of freedom per particle ($ \bar {Z} =
2 d_f$), does not apply to nonspherical particles. We
develop first- and second-order conditions for jamming
and demonstrate that packings of nonspherical particles
can be jammed even though they are underconstrained
(hypoconstrained, $ \bar {Z} < 2 d_f$). We apply an
algorithm using these conditions to computer-generated
hypoconstrained ellipsoid and ellipse packings and
demonstrate that our algorithm does produce jammed
packings, even close to the sphere point. We also
consider packings that are nearly jammed and draw
connections to packings of deformable (but stiff)
particles. Finally, we consider the jamming conditions
for nearly spherical particles and explain
quantitatively the behavior we observe in the vicinity
of the sphere point.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
pagecount = "32",
}
@Book{Gruber:2007:CDG,
author = "Peter M. Gruber",
title = "Convex and discrete geometry",
volume = "336",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 578",
year = "2007",
ISBN = "3-540-71132-5 (hardcover)",
ISBN-13 = "978-3-540-71132-2 (hardcover)",
LCCN = "QA639.5 .G78 2007",
MRclass = "52-02 (11-02 46B20 49-02 49J53 90C25)",
MRnumber = "2335496 (2008f:52001)",
MRreviewer = "Aleksandr Koldobsky",
bibdate = "Wed Jan 9 09:28:14 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Grundlehren der mathematischen Wissenschaften",
URL = "http://www.loc.gov/catdir/enhancements/fy0825/2007922936-b.html;
http://www.loc.gov/catdir/enhancements/fy0825/2007922936-d.html;
http://www.loc.gov/catdir/enhancements/fy0825/2007922936-t.html",
acknowledgement = ack-nhfb,
subject = "Convex geometry; Discrete geometry",
}
@InCollection{Hales:2007:EQR,
author = "Thomas C. {Hales}",
title = "Equidecomposable quadratic regions",
crossref = "Botana:2007:ADG",
pages = "24--38",
year = "2007",
DOI = "https://doi.org/10.1007/978-3-540-77356-6_2",
MRclass = "68U05 51M20 51M25 68T15",
bibdate = "Thu May 22 16:19:28 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
ZMnumber = "1195.68104",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
}
@InProceedings{Imamichi:2007:MSS,
author = "Takashi Imamichi and Hiroshi Nagamochi",
title = "A Multi-sphere Scheme for {$2$D} and {$3$D} Packing
Problems",
crossref = "Stutzle:2007:ESL",
pages = "207--211",
year = "2007",
DOI = "https://doi.org/10.1007/978-3-540-74446-7_19",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/sls/sls2007.html#ImamichiN07;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Article{Kuperberg:2007:OAP,
author = "Wlodzimierz Kuperberg",
title = "Optimal Arrangements in Packing Congruent Balls in a
Spherical Container",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "37",
number = "2",
pages = "205--212",
month = feb,
year = "2007",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-006-1303-6",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/dcg/dcg37.html#Kuperberg07;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@InProceedings{Nipkow:2007:FTG,
author = "Tobias Nipkow and Gertrud Bauer and Paula Schultz",
title = "{Flyspeck I}. {Tame} graphs",
crossref = "Furbach:2007:ART",
pages = "21--35",
year = "2007",
DOI = "https://doi.org/10.1007/11814771_4",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRclass = "52C17 (Packing and covering in n dimensions (discrete
geometry)); 68T15 (Theorem proving (deduction,
resolution, etc.))",
MRnumber = "2354670",
bibdate = "Thu May 22 15:38:33 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Lecture Notes in Computer Science",
ZMnumber = "1222.52018",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
}
@Article{Trovato:2007:SSO,
author = "Antonio Trovato and Trinh Xuan Hoang and Jayanth R.
Banavar and Amos Maritan",
title = "Symmetry, Shape, and Order",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "104",
number = "49",
pages = "19187--19192",
month = dec,
year = "2007",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.0707523104",
ISSN = "0027-8424",
ISSN-L = "0027-8424",
bibdate = "Fri Jun 7 05:51:55 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Article{Zammataro:2007:ECM,
author = "Luca Zammataro and Guido Serini and Todd Rowland and
Federico Bussolino",
title = "Embryonic cleavage modeling as a computational
approach to sphere packing problem",
journal = j-J-THEOR-BIOL,
volume = "245",
number = "1",
pages = "77--82",
year = "2007",
CODEN = "JTBIAP",
DOI = "https://doi.org/10.1016/j.jtbi.2006.09.032",
ISSN = "0022-5193",
ISSN-L = "0022-5193",
MRclass = "92C37 (52C17)",
MRnumber = "2306459 (2007m:92023)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00225193",
keywords = "Kepler sphere-packing conjecture",
}
@InCollection{Anikeenko:2008:SDS,
author = "Alexey V. Anikeenko and Marina L. Gavrilova and
Nikolai N. Medvedev",
title = "Shapes of {Delaunay} Simplexes and Structural Analysis
of Hard Sphere Packings",
crossref = "Gavrilova:2008:GVD",
volume = "158",
publisher = pub-SV,
address = pub-SV:adr,
pages = "13--45",
year = "2008",
DOI = "https://doi.org/10.1007/978-3-540-85126-4_2",
ISBN = "3-540-85125-9",
ISBN-13 = "978-3-540-85125-7",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/series/sci/sci158.html#AnikeenkoGM08;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Studies in Computational Intelligence",
acknowledgement = ack-nhfb,
}
@Article{Birgin:2008:MOD,
author = "Ernesto G. Birgin and F. N. C. Sobral",
title = "Minimizing the object dimensions in circle and sphere
packing problems",
journal = j-COMP-OP-RES,
volume = "35",
number = "7",
pages = "2357--2375",
year = "2008",
CODEN = "CMORAP",
DOI = "https://doi.org/10.1016/j.cor.2006.11.002",
ISSN = "0305-0548 (print), 1873-765X (electronic)",
ISSN-L = "0305-0548",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/cor/cor35.html#BirginS08;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Operations Research",
}
@Article{Chen:2008:DPR,
author = "Elizabeth R. Chen",
title = "A Dense Packing of Regular Tetrahedra",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "40",
number = "2",
pages = "214--240",
month = sep,
year = "2008",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-008-9101-y",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (52B10 52B55)",
MRnumber = "2438925 (2009g:52035)",
MRreviewer = "Marek Lassak",
bibdate = "Fri Aug 14 13:59:06 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.springerlink.com/content/f06j66h83424q440/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@InCollection{Chen:2008:SPP,
author = "Danny Z. Chen",
title = "Sphere Packing Problem",
crossref = "Kao:2008:EA",
year = "2008",
DOI = "https://doi.org/10.1007/978-0-387-30162-4_391",
bibdate = "Thu Aug 13 18:08:01 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/reference/algo/algo2008.html#Chen08;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Article{Hales:2008:FP,
author = "Thomas C. Hales",
title = "Formal Proof",
journal = j-NAMS,
volume = "55",
number = "11",
pages = "1370--1380",
month = dec,
year = "2008",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "03B35 (68T15)",
MRnumber = "2463990 (2010h:03012)",
MRreviewer = "Jean-Fran{\c{c}}ois Dufourd",
bibdate = "Wed Jan 09 07:49:58 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.ams.org/notices/200811/index.html;
http://www.ams.org/notices/200811/tx081101370p.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
keywords = "FPK (Formal Proof of the Kepler Conjecture); Project
Flyspeck",
remark = "There are three other related papers in this issue on
Formal Proof.",
}
@Article{Harrison:2008:FPT,
author = "John Harrison",
title = "Formal proof---theory and practice",
journal = j-NAMS,
volume = "55",
number = "11",
pages = "1395--1406",
year = "2008",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "03B35 (68T15)",
MRnumber = "2463992 (2010h:03013)",
MRreviewer = "Jean-Fran{\c{c}}ois Dufourd",
bibdate = "Thu May 22 15:23:56 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
keywords = "Project Flyspeck",
}
@Article{Scardicchio:2008:EOD,
author = "A. Scardicchio and F. H. Stillinger and S. Torquato",
title = "Estimates of the optimal density of sphere packings in
high dimensions",
journal = j-J-MATH-PHYS,
volume = "49",
number = "4",
pages = "043301",
month = apr,
year = "2008",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.2897027",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Wed Oct 26 09:05:55 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/jmathphys2005.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v49/i4/p043301_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "3 April 2008",
pagecount = "15",
}
@InCollection{Toth:2008:CCB,
author = "G{\'a}bor Fejes T{\'o}th",
booktitle = "Number theory \& discrete geometry",
title = "Covering with convex bodies",
volume = "6",
publisher = "Ramanujan Mathematical Society",
address = "Mysore, India",
pages = "181--189",
year = "2008",
MRclass = "52C17",
MRnumber = "2454307 (2010e:52046)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Ramanujan Math. Soc. Lect. Notes Ser.",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Cohn:2009:MPT,
author = "Henry Cohn",
title = "Mathematical physics: {A} tight squeeze",
journal = j-NATURE,
volume = "460",
number = "7257",
pages = "801--802",
day = "13",
month = aug,
year = "2009",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/460801a",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Thu Aug 13 16:53:32 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.nature.com/nature/journal/v460/n7257/;
http://www.princeton.edu/main/news/archive/S25/00/22A50/;
http://www.nature.com/nature/journal/v460/n7257/pdf/460801a.pdf",
abstract = "How can identical particles be crammed together as
densely as possible? A combination of theory and
computer simulations shows how the answer to this
intricate problem depends on the shape of the
particles.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "Advances in packing of tetrahedra and more complex
solids.",
}
@InCollection{Entezari:2009:SPT,
author = "Alireza Entezari and Ramsay Dyer and Torsten
M{\"o}ller",
booktitle = "Mathematical foundations of scientific visualization,
computer graphics, and massive data exploration",
title = "From sphere packing to the theory of optimal lattice
sampling",
publisher = pub-SV,
address = pub-SV:adr,
pages = "227--255",
year = "2009",
DOI = "https://doi.org/10.1007/b106657_12",
MRclass = "94A20 (52C17 65D18)",
MRnumber = "2560516 (2012i:94103)",
MRreviewer = "Jordi Marzo",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Math. Vis.",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Haji-Akbari:2009:DQC,
author = "Amir Haji-Akbari and Michael Engel and Aaron S. Keys
and Xiaoyu Zheng and Rolfe G. Petschek and Peter
Palffy-Muhoray and Sharon C. Glotzer",
title = "Disordered, quasicrystalline and crystalline phases of
densely packed tetrahedra",
journal = j-NATURE,
volume = "462",
number = "7274",
pages = "773--777",
day = "10",
month = dec,
year = "2009",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/nature08641",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Jan 09 09:34:06 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.nature.com/nature/journal/v462/n7274/full/nature08641.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
}
@Article{Jiao:2009:OPS,
author = "Y. Jiao and F. H. Stillinger and S. Torquato",
title = "Optimal packings of superballs",
journal = j-PHYS-REV-E,
volume = "79",
number = "4",
pages = "041309",
month = "????",
year = "2009",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.79.041309",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Fri Aug 14 17:20:44 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.79.041309",
abstract = "Dense hard-particle packings are intimately related to
the structure of low-temperature phases of matter and
are useful models of heterogeneous materials and
granular media. Most studies of the densest packings in
three dimensions have considered spherical shapes, and
it is only more recently that nonspherical shapes
(e.g., ellipsoids) have been investigated. Superballs
(whose shapes are defined by $ |x1 |^{2p} + |x2 |^{2p}
+ |x3 |^{2p} <= 1$) provide a versatile family of
convex particles ($ p \geq 0.5$) with both cubic-like
and octahedral-like shapes as well as concave particles
($ 0 < p < 0.5$) with octahedral-like shapes. In this
paper, we provide analytical constructions for the
densest known superball packings for all convex and
concave cases. The candidate maximally dense packings
are certain families of Bravais lattice packings (in
which each particle has 12 contacting neighbors)
possessing the global symmetries that are consistent
with certain symmetries of a superball. We also provide
strong evidence that our packings for convex superballs
($ p >= 0.5$) are most likely the optimal ones. The
maximal packing density as a function of $p$ is
nonanalytic at the sphere point ($ p = 1$) and
increases dramatically as p moves away from unity. Two
more nontrivial nonanalytic behaviors occur at $ p_c^*
>= 1.150 9...$ and $ p_o^* = \ln 3 / \ln 4 = 0.792
4...$ for cubic and octahedral superballs,
respectively, where different Bravais lattice packings
possess the same densities. The packing characteristics
determined by the broken rotational symmetry of
superballs are similar to but richer than their
two-dimensional superdisk counterparts [Y. Jiao et al.,
Phys. Rev. Lett. 100, 245504 (2008)] and are distinctly
different from that of ellipsoid packings. Our
candidate optimal superball packings provide a starting
point to quantify the equilibrium phase behavior of
superball systems, which should deepen our
understanding of the statistical thermodynamics of
nonspherical-particle systems.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
pagecount = "12",
}
@Article{Kallus:2009:DPP,
author = "Y. Kallus and V. Elser and S. Gravel",
title = "Dense periodic packings of tetrahedra with small
repeating units",
journal = "{arXiv.org}",
pages = "??",
day = "27",
month = oct,
year = "2009",
bibdate = "Wed Jan 09 10:04:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Published in \cite{Kallus:2010:DPP}.",
URL = "http://arxiv.org/abs/0910.5226",
acknowledgement = ack-nhfb,
}
@Article{Obua:2009:FIB,
author = "Steven Obua and Tobias Nipkow",
title = "{Flyspeck II}: the basic linear programs",
journal = j-ANN-MATH-ARTIF-INTELL,
volume = "56",
number = "3-4",
pages = "245--272",
year = "2009",
CODEN = "AMAIEC",
DOI = "https://doi.org/10.1007/s10472-009-9168-z",
ISSN = "1012-2443 (print), 1573-7470 (electronic)",
ISSN-L = "1012-2443",
MRclass = "68T15 (03B35)",
MRnumber = "2595204 (2011j:68135)",
bibdate = "Thu May 22 15:53:21 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics and Artificial Intelligence",
journal-URL = "http://link.springer.com/journal/10472",
keywords = "Project Flyspeck",
}
@Article{Schiftner:2009:PCS,
author = "Alexander Schiftner and Mathias H{\"o}binger and
Johannes Wallner and Helmut Pottmann",
title = "Packing circles and spheres on surfaces",
journal = j-TOG,
volume = "28",
number = "5",
pages = "139:1--139:8",
month = dec,
year = "2009",
CODEN = "ATGRDF",
DOI = "https://doi.org/10.1145/1661412.1618485",
ISSN = "0730-0301 (print), 1557-7368 (electronic)",
ISSN-L = "0730-0301",
bibdate = "Mon Mar 15 09:01:55 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/tog/;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
abstract = "Inspired by freeform designs in architecture which
involve circles and spheres, we introduce a new kind of
triangle mesh whose faces' incircles form a packing. As
it turns out, such meshes have a rich geometry and
allow us to cover surfaces with circle patterns, sphere
packings, approximate circle packings, hexagonal meshes
which carry a torsion-free support structure, hybrid
tri-hex meshes, and others. We show how triangle meshes
can be optimized so as to have the incircle packing
property. We explain their relation to conformal
geometry and implications on solvability of
optimization. The examples we give confirm that this
kind of meshes is a rich source of geometric structures
relevant to architectural geometry.",
acknowledgement = ack-nhfb,
articleno = "139",
fjournal = "ACM Transactions on Graphics",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J778",
keywords = "architectural geometry; circle packing; computational
conformal geometry; computational differential
geometry; freeform surface; sphere packing; supporting
structures",
}
@Article{Torquato:2009:ACF,
author = "S. Torquato and Y. Jiao",
title = "Analytical Constructions of a Family of Dense
Tetrahedron Packings and the Role of Symmetry",
journal = "{arXiv.org}",
pages = "16",
day = "21",
month = dec,
year = "2009",
bibdate = "Wed Jan 09 10:02:53 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://arxiv.org/abs/0912.4210",
acknowledgement = ack-nhfb,
}
@Article{Torquato:2009:DPPa,
author = "S. Torquato and Y. Jiao",
title = "Dense packings of the {Platonic} and {Archimedean}
solids",
journal = j-NATURE,
volume = "460",
number = "7257",
pages = "876--880",
day = "13",
month = aug,
year = "2009",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/nature08239",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Fri Aug 14 13:52:02 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.nature.com/nature/journal/v460/n7257/pdf/nature08239.pdf",
abstract = "Kepler's conjecture gives the densest possible packing
for spherical particles but, until now, there has not
been an analogous system for determining dense
polyhedral packings. Using a variety of multiparticle
initial configurations it has now been possible to
determine the densest known packings for the Platonic
solids and to conjecture that those of Platonic and
Archimedean solids with central symmetry are given by
their corresponding densest lattice packings.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
xxpages = "876--879",
}
@Article{Torquato:2009:DPPb,
author = "S. Torquato and Y. Jiao",
title = "Dense packings of polyhedra: {Platonic} and
{Archimedean} solids",
journal = j-PHYS-REV-E,
volume = "80",
number = "4",
pages = "041104:1--041104:21",
year = "2009",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.80.041104",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "52C17 (82D25)",
MRnumber = "2607418 (2010i:52027)",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
abstract = "Understanding the nature of dense particle packings is
a subject of intense research in the physical,
mathematical, and biological sciences. The
preponderance of previous work has focused on spherical
particles and very little is known about dense
polyhedral packings. We formulate the problem of
generating dense packings of nonoverlapping, nontiling
polyhedra within an adaptive fundamental cell subject
to periodic boundary conditions as an optimization
problem, which we call the adaptive shrinking cell
(ASC) scheme. This optimization problem is solved here
(using a variety of multiparticle initial
configurations) to find the dense packings of each of
the Platonic solids in three-dimensional Euclidean
space $ \mathbb {R}^3 $, except for the cube, which is
the only Platonic solid that tiles space. We find the
densest known packings of tetrahedra, icosahedra,
dodecahedra, and octahedra with densities 0.823\ldots,
0.836\ldots, 0.904\ldots, and 0.947\ldots,
respectively. It is noteworthy that the densest
tetrahedral packing possesses no long-range order.
Unlike the densest tetrahedral packing, which must not
be a Bravais lattice packing, the densest packings of
the other nontiling Platonic solids that we obtain are
their previously known optimal (Bravais) lattice
packings. We also derive a simple upper bound on the
maximal density of packings of congruent nonspherical
particles and apply it to Platonic solids, Archimedean
solids, superballs, and ellipsoids. Provided that what
we term the ``asphericity'' (ratio of the circumradius
to inradius) is sufficiently small, the upper bounds
are relatively tight and thus close to the
corresponding densities of the optimal lattice packings
of the centrally symmetric Platonic and Archimedean
solids. Our simulation results, rigorous upper bounds,
and other theoretical arguments lead us to the
conjecture that the densest packings of Platonic and
Archimedean solids with central symmetry are given by
their corresponding densest lattice packings. This can
be regarded to be the analog of Kepler's sphere
conjecture for these solids. The truncated tetrahedron
is the only non-centrally symmetric Archimedean solid,
the densest known packing of which is a non-lattice
packing with density at least as high as $ 23 / 24 =
0.958 ~333 ~ \ldots {} $. We discuss the validity of
our conjecture to packings of superballs, prisms, and
antiprisms as well as to high-dimensional analogs of
the Platonic solids. In addition, we conjecture that
the optimal packing of any convex, congruent polyhedron
without central symmetry generally is not a lattice
packing. Finally, we discuss the possible applications
and generalizations of the ASC scheme in predicting the
crystal structures of polyhedral nanoparticles and the
study of random packings of hard polyhedra.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Kepler sphere-packing conjecture",
PACS = "05.20.Jj; 45.70.An; 61.50.Ah",
}
@Article{vanMeel:2009:GFS,
author = "J. A. van Meel and D. Frenkel and P. Charbonneau",
title = "Geometrical frustration: a study of four-dimensional
hard spheres",
journal = j-PHYS-REV-E,
volume = "79",
number = "3",
pages = "030201",
month = mar,
year = "2009",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.79.030201",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Wed Feb 29 21:06:47 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.79.030201",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
numpages = "4",
}
@Article{Agapie:2010:RPH,
author = "Stefan C. Agapie and Paula A. Whitlock",
title = "Random packing of hyperspheres and {Marsaglia}'s
parking lot test",
journal = j-MONTE-CARLO-METHODS-APPL,
volume = "16",
number = "3--4",
pages = "197--209",
month = dec,
year = "2010",
CODEN = "MCMAC6",
DOI = "https://doi.org/10.1515/mcma.2010.019",
ISSN = "0929-9629 (print), 1569-3961 (electronic)",
ISSN-L = "0929-9629",
MRclass = "65C05 (65C10)",
MRnumber = "2747812",
bibdate = "Wed Feb 29 09:27:54 MST 2012",
bibsource = "http://www.degruyter.com/view/j/mcma.2010.16.issue-3/issue-files/mcma.2010.16.issue-3.xml;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/mcma.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.degruyter.com/view/j/mcma.2010.16.issue-3-4/mcma.2010.019/mcma.2010.019.xml",
acknowledgement = ack-nhfb,
fjournal = "Monte Carlo Methods and Applications",
journal-URL = "http://www.degruyter.com/view/j/mcma",
keywords = "CDC 48-bit multiplicative congruential generator {\tt
rannyu()}",
remark = "The authors investigate the connection between the
hypersphere packing problem and Marsaglia's parking lot
test \cite{Marsaglia:1985:CVR} for correlations in
random number generator output.",
}
@Article{Baker:2010:MMS,
author = "Jessica Baker and Arshad Kudrolli",
title = "Maximum and minimum stable random packings of
{Platonic} solids",
journal = j-PHYS-REV-E,
volume = "82",
number = "6 (part 1)",
pages = "061304",
month = dec,
year = "2010",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.82.061304",
ISSN = "1550-2376",
ISSN-L = "1539-3755",
bibdate = "Fri Jun 7 06:46:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Chen:2010:DCD,
author = "Elizabeth R. Chen and Michael Engel and Sharon C.
Glotzer",
title = "Dense crystalline dimer packings of regular
tetrahedra",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "44",
number = "2",
pages = "253--280",
month = sep,
year = "2010",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-010-9273-0",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "2671012 (2011k:52028)",
MRreviewer = "Peter M. Gruber",
bibdate = "Wed Jan 09 08:52:40 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@PhdThesis{Chen:2010:PTP,
author = "Elizabeth R. Chen",
title = "A picturebook of tetrahedral packings",
type = "{Ph.D.} Thesis",
school = "University of Michigan",
address = "Ann Arbor, MI. USA",
pages = "????",
year = "2010",
bibdate = "Wed Jan 09 08:47:42 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://hdl.handle.net/2027.42/75860;
http://mirlyn.lib.umich.edu/Record/008012603",
abstract = "We explore many different packings of regular
tetrahedra, with various clusters & lattices & symmetry
groups. We construct a dense packing of regular
tetrahedra, with packing density $ D > 0.7786157 $.",
acknowledgement = ack-nhfb,
}
@Article{Cox:2010:MPC,
author = "S. J. Cox and E. Flikkema",
title = "The minimal perimeter for {$N$} confined deformable
bubbles of equal area",
journal = j-ELECT-J-COMB,
volume = "17",
number = "1",
pages = "23",
year = "2010",
ISSN = "1077-8926 (print), 1097-1440 (electronic)",
ISSN-L = "1077-8926",
MRclass = "05B40 (52B05 52C17 74G65)",
MRnumber = "2607331 (2011e:05054)",
MRreviewer = "Ren Ding",
bibdate = "Wed Jan 9 16:40:33 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Research Paper 45.",
URL = "http://www.combinatorics.org/Volume_17/Abstracts/v17i1r45.html",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Combinatorics",
}
@Article{Hales:2010:DC,
author = "Thomas C. Hales and Sean McLaughlin",
title = "The dodecahedral conjecture",
journal = j-J-AM-MATH-SOC,
volume = "23",
number = "2",
pages = "299--344",
year = "2010",
DOI = "https://doi.org/10.1090/S0894-0347-09-00647-X",
ISSN = "0894-0347",
ISSN-L = "0894-0347",
MRclass = "52C17",
MRnumber = "2601036 (2011d:52037)",
MRreviewer = "Peter M. Gruber",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Mathematical Society",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Hales:2010:LPK,
author = "Thomas C. Hales",
title = "Linear Programs for the {Kepler} Conjecture",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6327",
pages = "149--151",
year = "2010",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_28",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRclass = "68-99 65-99",
bibdate = "Sat Aug 9 15:34:18 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_28.pdf",
ZMnumber = "05785562",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-15582-6",
book-URL = "http://www.springerlink.com/content/978-3-642-15582-6",
fjournal = "Lecture Notes in Computer Science",
keywords = "Project Flyspeck",
}
@Article{Hales:2010:RPK,
author = "Thomas C. Hales and John Harrison and Sean McLaughlin
and Tobias Nipkow and Steven Obua and Roland
Zumkeller",
title = "A revision of the proof of the {Kepler Conjecture}",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "44",
number = "1",
pages = "1--34",
year = "2010",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-009-9148-4",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17 (03B35 05B40 90C05)",
MRnumber = "2639816 (2012h:52044)",
MRreviewer = "Uwe Schnell",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "Kepler sphere-packing conjecture; Project Flyspeck",
}
@Article{Hopkins:2010:SCM,
author = "Adam B. Hopkins and Frank H. Stillinger and Salvatore
Torquato",
title = "Spherical codes, maximal local packing density, and
the golden ratio",
journal = j-J-MATH-PHYS,
volume = "51",
number = "4",
pages = "043302",
month = apr,
year = "2010",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.3372627",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Wed Oct 26 16:59:49 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
http://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v51/i4/p043302_s1",
acknowledgement = ack-nhfb,
journal-URL = "http://jmp.aip.org/",
onlinedate = "12 April 2010",
pagecount = "6",
}
@Article{Kallus:2010:DPP,
author = "Yoav Kallus and Veit Elser and Simon Gravel",
title = "Dense periodic packings of tetrahedra with small
repeating units",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "44",
number = "2",
pages = "245--252",
month = sep,
year = "2010",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-010-9254-3",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Wed Jan 09 09:41:04 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Li:2010:MPD,
author = "ShuiXiang Li and Jian Zhao and Peng Lu and Yu Xie",
title = "Maximum packing densities of basic {$3$D} objects",
journal = "Chinese Science Bulletin",
volume = "55",
number = "2",
pages = "114--119",
month = jan,
year = "2010",
DOI = "https://doi.org/10.1007/s11434-009-0650-0",
bibdate = "Fri Jun 7 05:51:55 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Chinese Science Bulletin",
}
@Article{Smith:2010:AJS,
author = "Kyle C. Smith and Meheboob Alam and Timothy S.
Fisher",
title = "Athermal jamming of soft frictionless {Platonic}
solids",
journal = j-PHYS-REV-E,
volume = "82",
number = "5 (part 1)",
pages = "051304",
month = nov,
year = "2010",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.82.051304",
ISSN = "1550-2376",
ISSN-L = "1539-3755",
bibdate = "Fri Jun 7 06:46:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Torquato:2010:DPP,
author = "S. Torquato and Y. Jiao",
title = "Dense packings of the {Platonic} and {Archimedean}
solids (vol 460, pg 876, 2009)",
journal = j-NATURE,
volume = "463",
number = "7284",
pages = "??--??",
month = "????",
year = "2010",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/nature08847",
ISSN = "0028-0836",
ISSN-L = "0028-0836",
bibdate = "Fri Jun 7 06:46:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
onlinedate = "2010-FEB-25",
}
@Article{Torquato:2010:ECF,
author = "S. Torquato and Y. Jiao",
title = "Exact constructions of a family of dense periodic
packings of tetrahedra",
journal = j-PHYS-REV-E,
volume = "81",
number = "4 (part 1)",
pages = "041310",
month = apr,
year = "2010",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.81.041310",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "82D25 (52C22)",
MRnumber = "2736208 (2012j:82052)",
bibdate = "Wed Jan 09 10:06:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Torquato:2010:JHP,
author = "S. Torquato and F. H. Stillinger",
title = "Jammed hard-particle packings: From {Kepler} to
{Bernal} and beyond",
journal = j-REV-MOD-PHYS,
volume = "82",
number = "3",
pages = "2633--2672",
month = jul,
year = "2010",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.82.2633",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
bibdate = "Tue May 22 16:37:33 MDT 2012",
bibsource = "http://rmp.aps.org/toc/RMP/v82/i3;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/revmodphys2010.bib",
note = "See note \cite{Torquato:2010:PNJ}.",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.82.2633;
http://rmp.aps.org/abstract/RMP/v82/i3/p2633_1",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
onlinedate = "15 September 2010",
}
@Article{Torquato:2010:PNJ,
author = "S. Torquato and F. H. Stillinger",
title = "{Publisher}'s Note: {Jammed hard-particle packings:
From Kepler to Bernal and beyond [Rev. Mod. Phys. {\bf
82}, 2633 (2010)]}",
journal = j-REV-MOD-PHYS,
volume = "82",
number = "4",
pages = "3197--3197",
month = oct,
year = "2010",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.82.3197",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
bibdate = "Tue May 22 16:37:34 MDT 2012",
bibsource = "http://rmp.aps.org/toc/RMP/v82/i4;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/revmodphys2010.bib",
note = "See \cite{Torquato:2010:JHP}.",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.82.3197;
http://rmp.aps.org/abstract/RMP/v82/i4/p3197_1",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
onlinedate = "20 December 2010",
}
@Article{Arkus:2011:DFS,
author = "Natalie Arkus and Vinothan N. Manoharan and Michael P.
Brenner",
title = "Deriving Finite Sphere Packings",
journal = j-SIAM-J-DISCR-MATH,
volume = "25",
number = "4",
pages = "1860--1901",
month = "????",
year = "2011",
CODEN = "SJDMEC",
DOI = "https://doi.org/10.1137/100784424",
ISSN = "0895-4801 (print), 1095-7146 (electronic)",
ISSN-L = "0895-4801",
bibdate = "Thu Feb 9 07:01:44 MST 2012",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIDMA/25/4;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/siamjdiscrmath.bib",
URL = "http://epubs.siam.org/sidma/resource/1/sjdmec/v25/i4/p1860_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Discrete Mathematics",
journal-URL = "http://epubs.siam.org/sidma",
onlinedate = "December 20, 2011",
}
@PhdThesis{Balou:2011:THT,
author = "A. Haji Akbari Balou",
title = "Thermodynamics of the hard tetrahedron system",
type = "{Ph.D.} thesis",
school = "University of Michigan",
address = "Ann Arbor, MI, USA",
pages = "????",
year = "2011",
bibdate = "Wed Jan 09 09:31:25 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://hdl.handle.net/2027.42/91590",
acknowledgement = ack-nhfb,
}
@Article{Fuchs:2011:SEI,
author = "Elena Fuchs and Katherine Sanden",
title = "Some Experiments with Integral {Apollonian} Circle
Packings",
journal = j-EXP-MATH,
volume = "20",
number = "4",
pages = "380--399",
month = "????",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2011.565255",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Mon Mar 5 15:46:22 MST 2012",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.tandfonline.com/toc/uexm20/20/4",
URL = "http://projecteuclid.org/euclid.em/1323367153",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "28 Nov 2011",
}
@Article{Gravel:2011:UBP,
author = "Simon Gravel and Veit Elser and Yoav Kallus",
title = "Upper bound on the packing density of regular
tetrahedra and octahedra",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "46",
number = "4",
pages = "799--818",
month = dec,
year = "2011",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/s00454-010-9304-x",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
MRclass = "52C17",
MRnumber = "2846180 (2012g:52035)",
MRreviewer = "W. Kuperberg",
bibdate = "Wed Jan 09 09:23:37 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Haji-Akbari:2011:PDH,
author = "Amir Haji-Akbari and Michael Engel and Sharon C.
Glotzer",
title = "Phase diagram of hard tetrahedra",
journal = j-J-CHEM-PHYS,
volume = "135",
number = "19",
pages = "194101:1--194101:10",
day = "15",
month = nov,
year = "2011",
CODEN = "JCPSA6",
DOI = "https://doi.org/10.1063/1.3651370",
ISSN = "0021-9606 (print), 1089-7690 (electronic)",
ISSN-L = "0021-9606",
bibdate = "Wed Jan 09 09:32:31 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://jcp.aip.org/resource/1/jcpsa6/v135/i19/p194101_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Chemical Physics",
journal-URL = "http://scitation.aip.org/content/aip/journal/jcp/browse",
}
@Book{Hales:2011:KC,
author = "Thomas Hales and Samuel Ferguson",
title = "The {Kepler Conjecture}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 456",
year = "2011",
ISBN = "1-4614-1128-9, 1-4614-1129-7",
ISBN-13 = "978-1-4614-1128-4; 978-1-4614-1129-1",
MRclass = "52-02 (11H31 52C17)",
MRnumber = "3075372",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "The Hales-Ferguson proof, Including papers reprinted
from Discrete Comput. Geom. {{\bf{3}}6} (2006), no. 1,
Edited by Jeffrey C. Lagarias",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Jiao:2011:MRJ,
author = "Yang Jiao and Salvatore Torquato",
title = "Maximally random jammed packings of {Platonic} solids:
hyperuniform long-range correlations and isostaticity",
journal = j-PHYS-REV-E,
volume = "84",
number = "4 (part 1)",
pages = "041309",
month = oct,
year = "2011",
CODEN = "PLEEE8",
ISSN = "1550-2376",
ISSN-L = "1539-3755",
bibdate = "Fri Jun 7 06:46:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@InCollection{Lagarias:2011:KCP,
author = "Jeffrey C. Lagarias",
title = "The {Kepler Conjecture} and its proof",
crossref = "Lagarias:2011:KCH",
chapter = "1",
publisher = pub-SV,
address = pub-SV:adr,
pages = "3--26",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4614-1129-1_1",
MRclass = "52C17 (11H31)",
MRnumber = "3050907",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
keywords = "Kepler sphere-packing conjecture",
}
@Article{Marchal:2011:SKC,
author = "Christian Marchal",
title = "Study of the {Kepler}'s conjecture: the problem of the
closest packing",
journal = j-MATH-Z,
volume = "267",
number = "3-4",
pages = "737--765",
year = "2011",
CODEN = "MAZEAX",
DOI = "https://doi.org/10.1007/s00209-009-0644-2",
ISSN = "0025-5874",
ISSN-L = "0025-5874",
MRclass = "52C17 (05B40)",
MRnumber = "2776056 (2012b:52032)",
MRreviewer = "M{\'a}rton Nasz{\'o}di",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Zeitschrift",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Andreanov:2012:RPL,
author = "A. Andreanov and A. Scardicchio",
title = "Random perfect lattices and the sphere packing
problem",
journal = j-PHYS-REV-E,
volume = "86",
number = "4 (part 1)",
pages = "041117",
month = oct,
year = "2012",
CODEN = "PLEEE8",
ISSN = "1550-2376",
ISSN-L = "1539-3755",
bibdate = "Fri Jun 7 07:03:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Gabbrielli:2012:FTS,
author = "Ruggero Gabbrielli and Yang Jiao and Salvatore
Torquato",
title = "Families of tessellations of space by elementary
polyhedra via retessellations of face-centered-cubic
and related tilings",
journal = j-PHYS-REV-E,
volume = "86",
number = "4 (part 1)",
pages = "041141",
month = oct,
year = "2012",
CODEN = "PLEEE8",
ISSN = "1550-2376",
ISSN-L = "1539-3755",
bibdate = "Fri Jun 7 06:46:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Garcke:2012:KKC,
author = "Harald Garcke",
title = "{Kepler, Kristalle und Computer. Mathematik und
numerische Simulationen helfen Kristallwachstum zu
verstehen}. ({German}) [{Kepler}, crystals and
computer. {Mathematics} and numerical simulations help
crystal-growth understanding]",
journal = j-MDMV,
volume = "20",
number = "4",
pages = "219--228",
year = "2012",
ISSN = "0947-4471",
MRclass = "52C17 (92E10)",
MRnumber = "3060788",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Mitteilungen der Deutschen Mathematiker-Vereinigung",
keywords = "Kepler sphere-packing conjecture",
language = "German",
}
@Book{Hales:2012:DSP,
author = "Thomas Callister Hales",
title = "Dense sphere packings: a blueprint for formal proofs",
volume = "400",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiv + 271",
year = "2012",
ISBN = "0-521-61770-7 (paperback)",
ISBN-13 = "978-0-521-61770-3 (paperback)",
LCCN = "QA166.7 .H35 2012",
bibdate = "Mon Aug 18 08:26:33 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "London Mathematical Society lecture note series",
abstract = "The 400-year-old Kepler Conjecture asserts that no
packing of congruent balls in three dimensions can have
a density exceeding the familiar pyramid-shaped
cannonball arrangement. In this book, a new proof of
the conjecture is presented that makes it accessible
for the first time to a broad mathematical audience.
The book also presents solutions to other previously
unresolved conjectures in discrete geometry, including
the strong dodecahedral conjecture on the smallest
surface area of a Voronoi cell in a sphere packing.
This book is also currently being used as a blueprint
for a large-scale formal proof project, which aims to
check every logical inference of the proof of the
Kepler conjecture by computer. This is an indispensable
resource for those who want to be brought up to date
with research on the Kepler Conjecture",
acknowledgement = ack-nhfb,
subject = "Sphere packings; Kepler's conjecture",
tableofcontents = "1. Close packing \\
2. Trigonometry \\
3. Volume \\
4. Hypermap \\
5. Fan \\
6. Packing \\
7. Local fan \\
8. Tame hypermap",
}
@Article{Joswig:2012:KHB,
author = "Michael Joswig",
title = "From {Kepler} to {Hales}, and back to {Hilbert}",
journal = j-DOC-MATH,
volume = "??",
pages = "439--446",
year = "2012",
ISSN = "1431-0635",
ISSN-L = "1431-0635",
MRclass = "01A65 (03B35 05B40 52-03 52C17)",
MRnumber = "2991505",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "Extra volume: Optimization stories.",
acknowledgement = ack-nhfb,
fjournal = "Documenta Mathematica",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Lagarias:2012:MPR,
author = "Jeffrey C. Lagarias and Chuanming Zong",
title = "Mysteries in Packing Regular Tetrahedra",
journal = j-NAMS,
volume = "59",
number = "11",
pages = "1540--1549",
month = dec,
year = "2012",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Wed Jan 09 07:36:55 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.ams.org/notices/201211/rtx121101540p.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
remark = "This article gives a nice historical survey of the
Kepler sphere-packing problem, and its extensions to
packing of Platonic solids, such as tetrahedra,
octahedra, cubeoctahedra, and icosahedra. It also shows
that several early `proofs' of their packing fractions
were wrong, and gives pointers to recent work that is
more reliable.",
}
@Article{Phillips:2012:OFS,
author = "Carolyn L. Phillips and Joshua A. Anderson and Greg
Huber and Sharon C. Glotzer",
title = "Optimal Filling of Shapes",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "11",
month = feb,
year = "2012",
bibdate = "Wed May 16 15:23:31 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "arXiv:1202.2450v1",
URL = "http://arxiv.org/abs/1202.2450;
http://www.rdmag.com/News/2012/05/Life-Science-Mathematics-Nanotechnology-Twist-on-ancient-math-problem-could-improve-medicine-microelectronics/",
abstract = "We present filling as a type of spatial subdivision
problem similar to covering and packing. Filling
addresses the optimal placement of overlapping objects
lying entirely inside an arbitrary shape so as to cover
the most interior volume. In $n$-dimensional space, if
the objects are polydisperse $n$-balls, we show that
solutions correspond to sets of maximal n-balls. For
polygons, we provide a heuristic for finding solutions
of maximal discs. We consider the properties of ideal
distributions of $N$ discs as $N$ approaches infinity.
We note an analogy with energy landscapes.",
acknowledgement = ack-nhfb,
pagecount = "5",
}
@Article{Ramezanpour:2012:CAS,
author = "A. Ramezanpour and R. Zecchina",
title = "Cavity approach to sphere packing in {Hamming} space",
journal = j-PHYS-REV-E,
volume = "85",
number = "2",
pages = "021106",
day = "6",
month = feb,
year = "2012",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.85.021106",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Mon Aug 6 10:20:20 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "https://link.aps.org/doi/10.1103/PhysRevE.85.021106",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
numpages = "16",
}
@Article{Torquato:2012:OPD,
author = "Salvatore Torquato and Yang Jiao",
title = "Organizing principles for dense packings of
nonspherical hard particles: not all shapes are created
equal",
journal = j-PHYS-REV-E,
volume = "86",
number = "1 (part 1)",
pages = "011102",
month = jul,
year = "2012",
CODEN = "PLEEE8",
ISSN = "1550-2376",
ISSN-L = "1539-3755",
bibdate = "Fri Jun 7 06:46:20 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@InProceedings{Allamigeon:2013:CBN,
author = "Xavier Allamigeon and St{\'e}phane Gaubert and Victor
Magron and Benjamin Werner",
title = "Certification of bounds of non-linear functions: the
templates method",
crossref = "Carette:2013:ICM",
pages = "51--65",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-39320-4_4",
MRclass = "68Txx",
bibdate = "Thu May 22 16:08:58 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
ZMnumber = "06197174",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
}
@Article{Bezdek:2013:SVK,
author = "K{\'a}roly Bezdek",
title = "On a strong version of the {Kepler Conjecture}",
journal = j-MATHEMATIKA,
volume = "59",
number = "1",
pages = "23--30",
year = "2013",
CODEN = "MTKAAB",
DOI = "https://doi.org/10.1112/S0025579312001039",
ISSN = "0025-5793",
MRclass = "52C22 (05B40 05B45 52B60 52C17)",
MRnumber = "3028169",
MRreviewer = "Brigitte Servatius",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematika. A Journal of Pure and Applied
Mathematics",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Chen:2013:GCL,
author = "Hao Chen",
title = "On a generalization of {Craig} lattices",
journal = "J. Th\'eor. Nombres Bordeaux",
volume = "25",
number = "1",
pages = "59--70",
year = "2013",
ISSN = "1246-7405",
MRclass = "11H31 (11H71 52C07 52C17)",
MRnumber = "3063830",
MRreviewer = "Ranjeet Kaur Sehmi",
bibdate = "Thu May 22 16:37:35 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://jtnb.cedram.org/item?id=JTNB_2013__25_1_59_0",
acknowledgement = ack-nhfb,
fjournal = "Journal de Th\'eorie des Nombres de Bordeaux",
keywords = "Kepler sphere-packing conjecture",
}
@Article{Harrison:2013:HLT,
author = "John Harrison",
title = "The {HOL Light} Theory of {Euclidean} Space",
journal = j-J-AUTOM-REASON,
volume = "50",
number = "2",
pages = "173--190",
month = feb,
year = "2013",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-012-9250-9",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
MRclass = "03B35 (68T15)",
MRnumber = "3016800",
bibdate = "Sat Apr 2 11:10:18 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jautomreason.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://link.springer.com/article/10.1007/s10817-012-9250-9",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
keywords = "Project Flyspeck",
}
@InProceedings{Kaliszyk:2013:ARS,
author = "Cezary Kaliszyk and Josef Urban",
title = "Automated reasoning service for {HOL Light}",
crossref = "Carette:2013:ICM",
pages = "120--135",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-39320-4_8",
MRclass = "68Txx",
bibdate = "Thu May 22 16:06:05 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
ZMnumber = "06197178",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
}
@Article{Li:2013:SCA,
author = "Yanheng Li and Wei Ji",
title = "Stability and convergence analysis of a dynamics-based
collective method for random sphere packing",
journal = j-J-COMPUT-PHYS,
volume = "250",
number = "??",
pages = "373--387",
day = "1",
month = oct,
year = "2013",
CODEN = "JCTPAH",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jul 8 16:59:11 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S002199911300363X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@InProceedings{Tankink:2013:FMD,
author = "Carst Tankink and Cezary Kaliszyk and Josef Urban and
Herman Geuvers",
title = "Formal mathematics on display: a {Wiki} for
{Flyspeck}",
crossref = "Carette:2013:ICM",
publisher = pub-SV,
address = pub-SV:adr,
pages = "152--167",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-39320-4_10",
ISBN = "3-642-39319-5 (paperback)",
ISBN-13 = "978-3-642-39319-8 (paperback)",
MRclass = "68Txx",
bibdate = "Thu May 22 15:56:15 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
ZMnumber = "06197180",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
}
@Article{Xu:2013:PPM,
author = "Bai-Xiang Xu and Yang Gao and Min-Zhong Wang",
title = "Particle packing and the mean theory",
journal = j-PHYS-LET-A,
volume = "377",
number = "3--4",
pages = "145--147",
year = "2013",
CODEN = "PYLAAG",
DOI = "https://doi.org/10.1016/j.physleta.2012.11.022",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Tue Mar 14 16:13:28 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/agm.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0375960112011772",
abstract = "This Letter presents two mean relations between the
densities/porosities of random and regular packing
modes. The two mean relations work very well for the
packing of spherical particles, cubic particles and
circular discs. Results confirm the corresponding
experimental and computational results.",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
keywords = "Arithmetic--geometric mean; Harmonic--geometric mean;
Packing density; Particle packing",
}
@Article{Zong:2013:TPD,
author = "Chuanming Zong",
title = "On the translative packing densities of tetrahedra and
cubooctahedra",
journal = "{arXiv.org}",
pages = "37",
day = "2",
month = aug,
year = "2013",
DOI = "",
bibdate = "Wed Jan 09 10:10:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://arxiv.org/abs/1208.0420",
abstract = "In this paper, upper bounds for the densities of the
densest translative tetrahedron packings and the
densest translative cubooctahedron packings are
obtained.",
acknowledgement = ack-nhfb,
}
@InProceedings{Adams:2014:FF,
author = "Mark Adams",
title = "Flyspecking {Flyspeck}",
crossref = "Hong:2014:MSI",
pages = "16--20",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2_3",
bibdate = "Tue Feb 06 10:26:02 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
abstract = "The formalisation of mathematics by use of theorem
provers has reached the stage where previously
questioned mathematical proofs have been formalised.
However, sceptics will argue that lingering doubts
remain about the efficacy of these formalisations. In
this paper we motivate and describe a capability for
addressing such concerns. We concentrate on the
nearly-complete Flyspeck Project, which uses the HOL
Light system to formalise the Kepler Conjecture proof.
We first explain why a sceptic might doubt the
formalisation. We go on to explain how the formal proof
can be ported to the highly-trustworthy HOL Zero system
and then independently audited, thus resolving any
doubts.",
acknowledgement = ack-nhfb,
}
@Article{Avigad:2014:FVM,
author = "Jeremy Avigad and John Harrison",
title = "Formally verified mathematics",
journal = j-CACM,
volume = "57",
number = "4",
pages = "66--75",
month = apr,
year = "2014",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2591012",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed May 21 10:20:09 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
abstract = "With the help of computational proof assistants,
formal verification could become the new standard for
rigor in mathematics.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "ACL2 proof system; Boyer--Moore NQTHM theorem prover;
Brouwer Fixed-Point Theorem; Coq proof system; de
Bruijn factor; EQP theorem prover; Four Color Theorem;
G{\"o}del Incompleteness Theorem; HOL proof system; HOL
Light proof system; Isabelle proof checker; LCF proof
checker; Milawa proof system; Mizar proof checker;
Nuprl proof system; Prime Number Theorem; Project
Flyspeck (Formal Proof of the Kepler Conjecture);
Prototype Verification System (PVS) proof system;
SSReflect proof language; Univalent Foundations
Project",
}
@Misc{Bailey:2014:FPC,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Formal proof completed for {Kepler}'s conjecture on
sphere packing",
howpublished = "Math Drudge",
day = "16",
month = aug,
year = "2014",
bibdate = "Tue May 15 15:05:09 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "https://experimentalmath.info/blog/2014/08/formal-proof-completed-for-keplers-conjecture-on-sphere-packing/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
}
@Article{deGoes:2014:WTG,
author = "Fernando de Goes and Pooran Memari and Patrick Mullen
and Mathieu Desbrun",
title = "Weighted Triangulations for Geometry Processing",
journal = j-TOG,
volume = "33",
number = "3",
pages = "28:1--28:??",
month = may,
year = "2014",
CODEN = "ATGRDF",
DOI = "https://doi.org/10.1145/2602143",
ISSN = "0730-0301 (print), 1557-7368 (electronic)",
ISSN-L = "0730-0301",
bibdate = "Mon Jun 9 12:26:19 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/tog/;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/tog.bib",
abstract = "In this article we investigate the use of weighted
triangulations as discrete, augmented approximations of
surfaces for digital geometry processing. By
incorporating a scalar weight per mesh vertex, we
introduce a new notion of discrete metric that defines
an orthogonal dual structure for arbitrary triangle
meshes and thus extends weighted Delaunay
triangulations to surface meshes. We also present
alternative characterizations of this primal-dual
structure (through combinations of angles, areas, and
lengths) and, in the process, uncover closed-form
expressions of mesh energies that were previously known
in implicit form only. Finally, we demonstrate how
weighted triangulations provide a faster and more
robust approach to a series of geometry processing
applications, including the generation of well-centered
meshes, self-supporting surfaces, and sphere packing.",
acknowledgement = ack-nhfb,
articleno = "28",
fjournal = "ACM Transactions on Graphics",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J778",
}
@Article{Hu:2014:RKP,
author = "Shengda Hu and Manuele Santoprete",
title = "Regularization of the {Kepler} Problem on the
Three-sphere",
journal = j-CAN-J-MATH,
volume = "66",
number = "4",
pages = "760--??",
month = aug,
year = "2014",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-2012-039-9",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 13 12:48:06 MDT 2014",
bibsource = "http://cms.math.ca/cjm/v66/n4;
http://www.math.utah.edu/pub/tex/bib/canjmath2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
abstract = "In this paper we regularize the Kepler problem on $
S^3 $ in several different ways. First, we perform a
Moser-type regularization. Then, we adapt the
Ligon-Schaaf regularization to our problem. Finally, we
show that the Moser regularization and the Ligon-Schaaf
map we obtained can be understood as the composition of
the corresponding maps for the Kepler problem in
Euclidean space and the gnomonic transformation.",
acknowledgement = ack-nhfb,
journal-URL = "http://cms.math.ca/cjm/",
}
@Article{NIST:2014:CDM,
author = "{NIST}",
title = "The clumping density of many things seems to be a
standard",
journal = j-RES-DEV,
volume = "??",
number = "??",
pages = "??--??",
day = "11",
month = jun,
year = "2014",
CODEN = "REDEEA",
ISSN = "0746-9179",
ISSN-L = "0746-9179",
bibdate = "Wed Jun 11 18:42:06 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "See research in \cite{Zangmeister:2014:PDR}",
URL = "http://www.rdmag.com/news/2014/06/nist-clumping-density-many-things-seems-be-standard",
abstract = "Particles of soot floating through the air and comets
hurtling through space have at least one thing in
common: 0.36. That, reports a research group at the
National Institute of Standards and Technology (NIST),
is the measure of how dense they will get under normal
conditions, and it s a value that seems to be constant
for similar aggregates across an impressively wide size
range from nanometers to tens of meters.",
acknowledgement = ack-nhfb,
fjournal = "Research \& Development",
}
@Article{Zangmeister:2014:PDR,
author = "Christopher D. Zangmeister and James G. Radney and
Lance T. Dockery and Jessica T. Young and Xiaofei Ma
and Rian You and Michael R. Zachariah",
title = "Packing density of rigid aggregates is independent of
scale",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2014",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.1403768111",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Sat Apr 8 10:47:39 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.pnas.org/content/early/2014/06/04/1403768111.abstract",
abstract = "Large planetary seedlings, comets, microscale
pharmaceuticals, and nanoscale soot particles are made
from rigid, aggregated subunits that are compacted
under low compression into larger structures spanning
over 10 orders of magnitude in dimensional space. Here,
we demonstrate that the packing density ($ \theta_f$)
of compacted rigid aggregates is independent of spatial
scale for systems under weak compaction. The $
\theta_f$ of rigid aggregated structures across six
orders of magnitude were measured using nanoscale
spherical soot aerosol composed of aggregates with
17-nm monomeric subunits and aggregates made from
uniform monomeric 6-mm spherical subunits at the
macroscale. We find $ \theta_f = 0.36 \pm 0.02$ at both
dimensions. These values are remarkably similar to $
\theta_f$ observed for comet nuclei and measured values
of other rigid aggregated systems across a wide variety
of spatial and formative conditions. We present a
packing model that incorporates the aggregate
morphology and show that $ \theta_f$ is independent of
both monomer and aggregate size. These observations
suggest that the $ \theta_f$ of rigid aggregates
subject to weak compaction forces is independent of
spatial dimension across varied formative conditions.",
eprint = "http://www.pnas.org/content/early/2014/06/04/1403768111.full.pdf+html",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Article{Zhang:2014:OAS,
author = "Yong Zhang and Francis Y. L. Chin and Hing-Fung Ting
and Xin Han and Chung Keung Poon and Yung H. Tsin and
Deshi Ye",
title = "Online algorithms for $1$-space bounded
$2$-dimensional bin packing and square packing",
journal = j-THEOR-COMP-SCI,
volume = "554",
number = "??",
pages = "135--149",
day = "16",
month = oct,
year = "2014",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Fri Oct 31 17:22:55 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/tcs2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304397514001716",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975/",
}
@Article{Hales:2015:FPK,
author = "Thomas Hales and Mark Adams and Gertrud Bauer and Dat
Tat Dang and John Harrison and Truong Le Hoang and
Cezary Kaliszyk and Victor Magron and Sean McLaughlin
and Thang Tat Nguyen and Truong Quang Nguyen and Tobias
Nipkow and Steven Obua and Joseph Pleso and Jason Rute
and Alexey Solovyev and An Hoai Thi Ta and Trung Nam
Tran and Diep Thi Trieu and Josef Urban and Ky Khac Vu
and Roland Zumkeller",
title = "A formal proof of the {Kepler} conjecture",
journal = "ArXiv.org",
pages = "21",
month = jan,
year = "2015",
bibdate = "Tue Jul 5 07:04:31 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://arxiv.org/abs/1501.02155",
abstract = "This article describes a formal proof of the Kepler
conjecture on dense sphere packings in a combination of
the HOL Light and Isabelle proof assistants. This paper
constitutes the official published account of the now
completed Flyspeck project.",
acknowledgement = ack-nhfb,
keywords = "Mathematics --- Metric Geometry, Computer Science ---
Logic in Computer Science",
primaryclass = "math.MG",
}
@Article{Khirevich:2015:CFG,
author = "Siarhei Khirevich and Irina Ginzburg and Ulrich
Tallarek",
title = "Coarse- and fine-grid numerical behavior of {MRT\slash
TRT} lattice-{Boltzmann} schemes in regular and random
sphere packings",
journal = j-J-COMPUT-PHYS,
volume = "281",
number = "??",
pages = "708--742",
day = "15",
month = jan,
year = "2015",
CODEN = "JCTPAH",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Nov 29 05:07:36 MST 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999114007207",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Misc{Bailey:2016:SPP,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Sphere packing problem solved in $8$ and $24$
dimensions",
howpublished = "Blog posting",
day = "1",
month = apr,
year = "2016",
bibdate = "Sat Apr 02 06:35:18 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "See research papers
\cite{Viazovska:2016:SPP,Cohn:2016:SPP}.",
URL = "http://experimentalmath.info/blog/2016/04/sphere-packing-problem-solved-in-8-and-24-dimensions/",
acknowledgement = ack-nhfb,
}
@Article{Cohn:2016:SPP,
author = "Henry Cohn and Abhinav Kumar and Stephen D. Miller and
Danylo Radchenko and Maryna Viazovska",
title = "The sphere packing problem in dimension $24$",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--12",
day = "21",
month = mar,
year = "2016",
bibdate = "Sat Apr 02 06:35:47 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://arxiv.org/abs/1603.06518",
acknowledgement = ack-nhfb,
}
@Article{Edwards:2016:NAP,
author = "Chris Edwards",
title = "News: Automating proofs",
journal = j-CACM,
volume = "59",
number = "4",
pages = "13--15",
month = apr,
year = "2016",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2892710",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Apr 15 14:58:10 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://cacm.acm.org/magazines/2016/4/200157/fulltext",
abstract = "Math struggles with the usability of formal proofs.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "Archive of Formal Proofs; Coq theorem prover;
Four-Color Theorem; Isabelle theorem prover; Kepler
Theorem; Project Flyspeck; Thomas Hales",
}
@Article{Holmes-Cerfon:2016:ERS,
author = "Miranda C. Holmes-Cerfon",
title = "Enumerating Rigid Sphere Packings",
journal = j-SIAM-REVIEW,
volume = "58",
number = "2",
pages = "229--244",
month = "????",
year = "2016",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/140982337",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri May 27 07:15:57 MDT 2016",
bibsource = "http://epubs.siam.org/toc/siread/58/2;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2016",
}
@Article{Lozano:2016:EAG,
author = "Elias Lozano and Deane Roehl and Waldemar Celes and
Marcelo Gattass",
title = "An efficient algorithm to generate random sphere packs
in arbitrary domains",
journal = j-COMPUT-MATH-APPL,
volume = "71",
number = "8",
pages = "1586--1601",
month = apr,
year = "2016",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:51:55 MST 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122116300864",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Misc{Pinter:2016:GOF,
author = "Janos Pinter and Frank J. Kampas and Ignacio
Castillo",
title = "Globally Optimized Finite Packings of Arbitrary Size
Spheres in {$ R^d $}",
howpublished = "Web document",
day = "31",
month = mar,
year = "2016",
bibdate = "Tue Apr 05 06:49:15 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.optimization-online.org/DB_HTML/2016/03/5392.html",
abstract = "This work discusses the following general packing
problem-class: given a finite collection of
$d$-dimensional spheres with arbitrarily chosen radii,
find the smallest sphere in R^d that contains the
entire collection of these spheres in a non-overlapping
arrangement. Generally speaking, analytical solution
approaches cannot be expected to apply to this general
problem-type, except for very small or certain
specially structured sphere configurations. In order to
find high-quality numerical (approximate) solutions, we
propose a suitable combination of heuristic strategies
with constrained global and local nonlinear
optimization. We present numerical results for
non-trivial model instance-classes of optimized sphere
configurations with up to $ n = 50$ spheres in
dimensions $ d = 2, 3, 4$. Our numerical results for an
intensively studied model-class in $ R^2$ are on
average within 1\% of the entire set of best known
results, with new optimized (conjectured) packings for
previously unexplored generalizations of the same
model-class in $ R^d$ with $ d = 3, 4$. The results
obtained also support the estimation of the optimized
container sphere radii and of the packing fraction as
functions of the model instance parameters $n$ and $ 1
/ n$, respectively.",
acknowledgement = ack-nhfb,
}
@Article{Viazovska:2016:SPP,
author = "Maryna Viazovska",
title = "The sphere packing problem in dimension $8$",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--22",
day = "14",
month = mar,
year = "2016",
bibdate = "Sat Apr 02 06:35:47 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://arxiv.org/abs/1603.04246",
acknowledgement = ack-nhfb,
}
@Article{Zauner:2016:AFF,
author = "Thomas Zauner",
title = "Application of a force field algorithm for creating
strongly correlated multiscale sphere packings",
journal = j-J-COMPUT-PHYS,
volume = "313",
number = "??",
pages = "662--673",
day = "15",
month = may,
year = "2016",
CODEN = "JCTPAH",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Tue Apr 5 16:33:45 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys2015.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999116001029",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Cohn:2017:CBS,
author = "Henry Cohn",
title = "A Conceptual Breakthrough in Sphere Packing",
journal = j-NAMS,
volume = "64",
number = "2",
pages = "102--115",
month = feb,
year = "2017",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Mon Jan 30 16:21:57 2017",
bibdate = "Mon Jan 30 16:18:54 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.ams.org/publications/journals/notices/201702/rnoti-p102.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
keywords = "8-D sphere-packing problem; Kepler 3-D sphere-packing
problem; Maryna Viazovska",
}
@Article{Degond:2017:DAH,
author = "Pierre Degond and Marina A. Ferreira and Sebastien
Motsch",
title = "{Damped Arrow-Hurwicz} algorithm for sphere packing",
journal = j-J-COMPUT-PHYS,
volume = "332",
number = "??",
pages = "47--65",
day = "1",
month = mar,
year = "2017",
CODEN = "JCTPAH",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Fri Jan 6 14:09:06 MST 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jcomputphys2015.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999116306398",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{He:2017:RSP,
author = "Xu He",
title = "Rotated Sphere Packing Designs",
journal = j-J-AM-STAT-ASSOC,
volume = "112",
number = "520",
pages = "1612--1622",
year = "2017",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.1080/01621459.2016.1222289",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Tue Mar 12 16:38:57 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jamstatassoc2010.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.tandfonline.com/toc/uasa20/112/520",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
onlinedate = "18 Jul 2017",
}
%%% ====================================================================
%%% Cross-referenced entries must come last:
@Book{Steele:1992:PA,
editor = "John Michael Steele and William F. Eddy",
title = "Probability and Algorithms",
publisher = pub-NAP,
address = pub-NAP:adr,
pages = "ix + 178",
year = "1992",
ISBN = "0-309-04776-5",
ISBN-13 = "978-0-309-04776-0",
LCCN = "QA273.P7953 1992",
bibdate = "Wed Jan 9 18:09:54 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
jenson.stanford.edu:2210/unicorn;
library.mit.edu:9909/mit01",
URL = "http://site.ebrary.com/lib/stanford/Doc?id=10056784;
http://www.nap.edu/books/0309047765/html/",
acknowledgement = ack-nhfb,
remark = "Panel on Probability and Algorithms, J. Michael
Steele, chair.. Committee on Applied and Theoretical
Statistics, William F. Eddy, chair.",
subject = "Probabilities; Algorithms; Combinatorial
optimization",
tableofcontents = "1: Introduction / J. Michael Steele and David
Aldous \\
2: Simulated Annealing / Dimitris Bertsimas and John
Tsitsiklis \\
3: Approximate Counting Via Markov Chains / David
Aldous \\
4: Probabilistic Algorithms for Speedup / Joan
Feigenbaum and Jeffrey C. Lagarias \\
5: Probabilistic Algorithms for Defeating Adversaries /
Joan Feigenbaum \\
6: Pseudorandom Numbers / Jeffrey C. Lagarias \\
7: Probabilistic Analysis of Packing and Related
Partitioning Problems / E. G. Coffman, Jr., D. S.
Johnson, P. W. Shor and G. S. Lueker \\
8: Probability and Problems in Euclidean Combinatorial
Optimization / J. Michael Steele \\
9: Probabilistic Analysis in Linear Programming / Ron
Shamir \\
10: Randomization in Parallel Algorithms / Vijaya
Ramachandran \\
11: Randomly Wired Multistage Networks / Bruce M. Maggs
\\
12: Missing Pieces, Derandomization, and Concluding
Remarks / J. Michael Steele",
}
@Proceedings{Billard:1985:CSS,
editor = "L. (Lynne) Billard",
booktitle = "Computer science and statistics: proceedings of the
Sixteenth Symposium on the Interface, Atlanta, Georgia,
March 1984",
title = "Computer science and statistics: proceedings of the
Sixteenth Symposium on the Interface, Atlanta, Georgia,
March 1984",
publisher = pub-ELS,
address = pub-ELS:adr,
bookpages = "xi + 296",
pages = "xi + 296",
year = "1985",
ISBN = "0-444-87725-8",
ISBN-13 = "978-0-444-87725-3",
LCCN = "QA276.4 .S95 1984",
bibdate = "Thu Dec 18 13:41:50 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
acknowledgement = ack-nhfb,
}
@Book{Gruber:1993:HCG,
editor = "Peter M. Gruber and J{\"o}rg M. Wills",
booktitle = "Handbook of Convex Geometry",
title = "Handbook of Convex Geometry",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xi + 735 (vol. A), lxvi + 739--1438 (vol. B)",
year = "1993",
ISBN = "0-444-89598-1 (set of vols. A and B), 0-444-89596-5
(vol. A), 0-444-89597-3 (vol. B)",
ISBN-13 = "978-0-444-89598-1 (set of vols. A and B),
978-0-444-89596-7 (vol. A), 978-0-444-89597-4 (vol.
B)",
LCCN = "QA639.5 .H36 1993",
bibdate = "Wed Jan 9 08:55:44 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Convex geometry",
xxpages = "xi + 1438",
xxpages = "xlvi + 735 (vol. A), lxvi + 739--1438 (vol. B)",
xxpages = "lxvi + 735 (vol. A), lxvi + 739--1438 (vol. B)",
}
@Book{Conway:1999:SPL,
editor = "John Horton Conway and N. J. A. (Neil James Alexander)
Sloane",
booktitle = "Sphere packings, lattices, and groups",
title = "Sphere packings, lattices, and groups",
volume = "290",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
pages = "lxxiv + 703",
year = "1999",
ISBN = "0-387-98585-9 (hardcover)",
ISBN-13 = "978-0-387-98585-5 (hardcover)",
LCCN = "QA166.7 .C66 1999; QA3 .G75",
bibdate = "Fri Aug 14 17:15:48 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
melvyl.cdlib.org:210/CDL90",
series = "Grundlehren der mathematischen Wissenschaften",
acknowledgement = ack-nhfb,
remark = "Ch. 1. Sphere Packings and Kissing Numbers / J. H.
Conway and N. J. A. Sloane \\
Ch. 2. Coverings, Lattices and Quantizers / J. H.
Conway and N. J. A. Sloane \\
Ch. 3. Codes, Designs and Groups / J. H. Conway and N.
J. A. Sloane \\
Ch. 4. Certain Important Lattices and Their Properties
/ J. H. Conway and N. J. A. Sloane \\
Ch. 5. Sphere Packing and Error-Correcting Codes / J.
Leech and N. J. A. Sloane \\
Ch. 6. Laminated Lattices / J. H. Conway and N. J. A.
Sloane \\
Ch. 7. Further Connections Between Codes and Lattices /
N. J. A. Sloane \\
Ch. 8. Algebraic Constructions for Lattices / J. H.
Conway and N. J. A. Sloane \\
Ch. 9. Bounds for Codes and Sphere Packings / N. J. A.
Sloane \\
Ch. 10. Three Lectures on Exceptional Groups / J. H.
Conway \\
Ch. 11. The Golay Codes and the Mathieu Groups / J. H.
Conway \\
Ch. 12. A Characterization of the Leech Lattice / J. H.
Conway \\
Ch. 13. Bounds on Kissing Numbers / A. M. Odlyzko and
N. J. A. Sloane\ldots{} Ch. 14. Uniqueness of Certain
Spherical Codes / E. Bannai and N. J. A. Sloane \\
Ch. 15. On the Classification of Integral Quadratic
Forms / J. H. Conway and N. J. A. Sloane \\
Ch. 16. Enumeration of Unimodular Lattices / J. H.
Conway and N. J. A. Sloane \\
Ch. 17. The 24-Dimensional Odd Unimodular Lattices / R.
E. Borcherds \\
Ch. 18. Even Unimodular 24-Dimensional Lattices / B. B.
Venkov \\
Ch. 19. Enumeration of Extremal Self-Dual Lattices / J.
H. Conway, A. M. Odlyzko and N. J. A. Sloane \\
Ch. 20. Finding the Closest Lattice Point / J. H.
Conway and N. J. A. Sloane \\
Ch. 21. Voronoi Cells of Lattices and Quantization
Errors / J. H. Conway and N. J. A. Sloane \\
Ch. 22. A Bound for the Covering Radius of the Leech
Lattice / S. P. Norton \\
Ch. 23. The Covering Radius of the Leech Lattice / J.
H. Conway, R. A. Parker and N. J. A. Sloane \\
Ch. 24. Twenty-Three Constructions for the Leech
Lattice / J. H. Conway and N. J. A. Sloane\ldots{} Ch.
25. The Cellular Structure of the Leech Lattice / R. E.
Borcherds, J. H. Conway and L. Queen \\
Ch. 26. Lorentzian Forms for the Leech Lattice / J. H.
Conway and N. J. A. Sloane \\
Ch. 27. The Automorphism Group of the 26-Dimensional
Even Unimodular Lorentzian Lattice / J. H. Conway \\
Ch. 28. Leech Roots and Vinberg Groups / J. H. Conway
and N. J. A. Sloane \\
Ch. 29. The Monster Group and its 196884-Dimensional
Space / J. H. Conway \\
Ch. 30. A Monster Lie Algebra? / R. E. Borcherds, J. H.
Conway and L. Queen [et al.]",
subject = "combinatorial packing and covering; sphere; lattice
theory; finite groups",
xxauthor = "John Horton Conway and N. J. A. (Neil James Alexander)
Sloane and Eiichi Bannai and others",
}
@Proceedings{ACM:2001:PSA,
editor = "ACM",
booktitle = "{Proceedings of the seventeenth annual Symposium on
Computational Geometry (SCG'01): June 3--5, 2001,
Medford, Massachusetts, USA}",
title = "{Proceedings of the seventeenth annual Symposium on
Computational Geometry (SCG'01): June 3--5, 2001,
Medford, Massachusetts, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 334",
year = "2001",
ISBN = "1-58113-357-X",
ISBN-13 = "978-1-58113-357-8",
LCCN = "????",
bibdate = "Fri Jan 6 12:10:47 MST 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
library.ox.ac.uk:210/ADVANCE",
acknowledgement = ack-nhfb,
remark = "ACM order number 429010.",
subject = "Geometry; Data processing; Congresses",
}
@Proceedings{Amir:2001:CPM,
editor = "Amihood Amir and Gad M. Landau",
booktitle = "{Combinatorial pattern matching: 12th annual
symposium, CPM 2001, Jerusalem, Israel, July 1--4,
2001: Proceedings}",
title = "{Combinatorial pattern matching: 12th annual
symposium, CPM 2001, Jerusalem, Israel, July 1--4,
2001: Proceedings}",
volume = "2089",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 271",
year = "2001",
CODEN = "LNCSD9",
DOI = "????",
ISBN = "3-540-42271-4",
ISBN-13 = "978-3-540-42271-6",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.A43 C65 2001",
bibdate = "Thu Jan 17 11:49:19 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = ser-LNCS # " and " # ser-LNAI,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2089.htm;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2089",
acknowledgement = ack-nhfb,
keywords = "combinatorial analysis --- congresses; computer
algorithms --- congresses",
}
@Book{Gardner:2001:CBM,
author = "Martin Gardner",
booktitle = "The colossal book of mathematics: classic puzzles,
paradoxes, and problems: number theory, algebra,
geometry, probability, topology, game theory, infinity,
and other topics of recreational mathematics",
title = "The colossal book of mathematics: classic puzzles,
paradoxes, and problems: number theory, algebra,
geometry, probability, topology, game theory, infinity,
and other topics of recreational mathematics",
publisher = pub-NORTON,
address = pub-NORTON:adr,
pages = "xi + 724",
year = "2001",
ISBN = "0-393-02023-1",
ISBN-13 = "978-0-393-02023-6",
LCCN = "QA95 .G245 2001",
bibdate = "Wed Jan 9 17:40:28 MST 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1914--2010",
subject = "Mathematical recreations",
tableofcontents = "Preface \\
I. Arithmetic and algebra \\
1. The monkey and the coconuts \\
2. The calculus of finite differences \\
3. Palindromes : words and numbers \\
II. Plane geometry \\
4. Curves of constant width \\
5. Rep-tiles \\
6. Piet Hein's superellipse \\
7. Penrose tiles \\
8. The wonders of a planiverse \\
III. Solid geometry and higher dimensions \\
9. The helix \\
10. Packing spheres \\
11. Spheres and hyperspheres \\
12. The Church of the Fourth Dimension \\
13. Hypercubes \\
14. Non-Euclidean geometry \\
IV. Symmetry \\
15. Rotations and reflections \\
16. The amazing creations of Scott Kim \\
17. The art of M. C. Escher \\
V. Topology \\
18. Klein bottles and other surfaces \\
19. Knots \\
20. Doughnuts : linked and knotted \\
VI. Probability \\
21. Probability and ambiguity \\
22. Nontransitive dice and other paradoxes \\
23. More nontransitive paradoxes \\
VII. Infinity \\
24. Infinite regress \\
25. Aleph-null and aleph-one \\
26. Supertasks \\
27. Fractal music \\
28. Surreal numbers \\
VIII. Combinatorics \\
29. Hexaflexagons \\
30. The Soma cube \\
31. The game of life \\
32. Paper folding \\
33. Ramsey theory \\
34. Bulgarian solitaire and other seemingly endless
tasks \\
IX. Games and decision theory \\
35. A matchbox game-learning machine \\
36. Sprouts and Brussels sprouts \\
37. Harary's generalized ticktacktoe \\
38. The new Eleusis \\
X. Physics \\
39. Time travel \\
40. Does time ever stop? \\
41. Induction and probability \\
42. Simplicity \\
XI. Logic and philosophy \\
43. The unexpected hanging \\
44. Newcomb's paradox \\
45. Nothing \\
46. Everything \\
XII. Miscellaneous \\
47. Melody-making machines \\
48. Mathematical zoo \\
49. G{\"o}del, Escher, Bach \\
50. Six sensational discoveries \\
Selected titles by the author on mathematics \\
Index",
}
@Book{March:2002:ILS,
author = "Norman H. (Norman Henry) March and M. P. Tosi",
booktitle = "Introduction to Liquid State Physics",
title = "Introduction to Liquid State Physics",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xvii + 431",
year = "2002",
DOI = "https://doi.org/10.1142/4717",
ISBN = "981-02-4652-8 (paperback), 981-02-4639-0,
981-277-848-9 (e-book)",
ISBN-13 = "978-981-277-848-2 (e-book), 978-981-02-4652-5
(paperback), 978-981-02-4639-6",
LCCN = "QC145.2 .M42 2002eb",
bibdate = "Tue May 28 14:24:20 MDT 2013",
bibsource = "aubrey.tamu.edu:7090/voyager;
catalog.princeton.edu:7090/voyager;
clas.caltech.edu:210/INNOPAC;
fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/m/march-norman-h.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
jenson.stanford.edu:2210/unicorn;
prodorbis.library.yale.edu:7090/voyager",
URL = "http://site.ebrary.com/lib/princeton/Doc?id=10201245;
http://site.ebrary.com/lib/yale/Doc?id=10201245;
http://www.worldscientific.com/worldscibooks/10.1142/4717",
acknowledgement = ack-nhfb,
subject = "Liquids; Thermodynamics; Statistical mechanics;
SCIENCE; Physics; General;Mechanics; Energy",
}
@Proceedings{McKay:2002:AAA,
editor = "Bob McKay and J. K. Slaney",
booktitle = "{AI 2002}: advances in artificial intelligence: 15th
Australian Joint Conference on Artificial Intelligence,
Canberra, Australia, December 2--6, 2002: Proceedings",
title = "{AI 2002}: advances in artificial intelligence: 15th
Australian Joint Conference on Artificial Intelligence,
Canberra, Australia, December 2--6, 2002: Proceedings",
volume = "2557",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 730",
year = "2002",
CODEN = "LNCSD9",
DOI = "????",
ISBN = "3-540-00197-2 (paperback)",
ISBN-13 = "978-3-540-00197-3 (paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "Q334 .A97 2002",
bibdate = "Thu Nov 11 19:26:30 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = ser-LNAI # " and " # ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2557.htm;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2557",
acknowledgement = ack-nhfb,
keywords = "artificial intelligence --- congresses",
}
@Proceedings{Sloot:2002:CSIc,
editor = "P. M. A. Sloot and C. J. Kenneth Tan and J. J.
Dongarra and A. G. Hoekstra",
booktitle = "Computational Science--ICCS 2002: International
Conference, Amsterdam, The Netherlands, April 21--24,
2002. Proceedings, Part III",
title = "Computational Science--{ICCS 2002}: International
Conference, Amsterdam, The Netherlands, April 21--24,
2002. Proceedings, {Part III}",
volume = "2331",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xli + 1227",
year = "2002",
CODEN = "LNCSD9",
ISBN = "3-540-43594-8 (paperback)",
ISBN-13 = "978-3-540-43594-5 (paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA75.5 .I13 2002",
bibdate = "Thu Nov 11 19:26:30 MST 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2331.htm",
acknowledgement = ack-nhfb,
}
@Proceedings{Slind:2004:TPH,
editor = "Konrad Slind and Annette Bunker and Ganesh
Gopalakrishnan",
booktitle = "{Theorem proving in higher order logics: 17th
international conference, TPHOLs 2004, Park City, Utah,
USA, September 14--17, 2004: proceedings}",
title = "{Theorem proving in higher order logics: 17th
international conference, TPHOLs 2004, Park City, Utah,
USA, September 14--17, 2004: proceedings}",
volume = "3223",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 336",
year = "2004",
DOI = "https://doi.org/10.1007/b100400",
ISBN = "3-540-23017-3 (paperback)",
ISBN-13 = "978-3-540-23017-5 (paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.A96 T655 2004",
MRclass = "68-06 (03B15 03B35 68T15)",
MRnumber = "2142103 (2005m:68012)",
bibdate = "Thu Aug 13 17:35:01 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Lecture notes in computer science",
URL = "http://www.loc.gov/catdir/enhancements/fy0823/2004111288-d.html;
http://www.loc.gov/catdir/summary/eng0801/2004111288.html;
http://www.loc.gov/catdir/toc/fy0716/2004111288.html;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=3223",
acknowledgement = ack-nhfb,
meetingname = "TPHOLs 2004 (2004 : Park City, Utah)",
subject = "Automatic theorem proving; Congresses",
}
@Proceedings{Hurd:2005:TPH,
editor = "Joe Hurd and T. F. (Tom F.) Melham",
booktitle = "{Theorem proving in higher order logics: 18th
international conference, TPHOLs 2005, Oxford, UK,
August 22--25, 2005: proceedings}",
title = "{Theorem proving in higher order logics: 18th
international conference, TPHOLs 2005, Oxford, UK,
August 22--25, 2005: proceedings}",
volume = "3603",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 408",
year = "2005",
ISBN = "3-540-28372-2 (paperback)",
ISBN-13 = "978-3-540-28372-0 (paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.A96 T655 2005",
bibdate = "Thu May 22 16:23:45 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
series = "Lecture notes in computer science",
URL = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0302-9743&volume=3603;
http://www.loc.gov/catdir/enhancements/fy0663/2005930490-d.html;
http://www.loc.gov/catdir/toc/fy0612/2005930490.html",
acknowledgement = ack-nhfb,
meetingname = "TPHOLs 2005 (2005 : Oxford, England)",
subject = "Automatic theorem proving; Congresses",
}
@Proceedings{Botana:2007:ADG,
editor = "Francisco Botana and Tomas Recio",
booktitle = "{Automated deduction in geometry: 6th international
workshop, ADG 2006, Pontevedra, Spain, August
31--September 2, 2006. revised papers}",
title = "{Automated deduction in geometry: 6th international
workshop, ADG 2006, Pontevedra, Spain, August
31--September 2, 2006. revised papers}",
volume = "4869",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 211",
year = "2007",
DOI = "https://doi.org/10.1007/978-3-540-77356-6",
ISBN = "3-540-77355-X (softcover)",
ISBN-13 = "978-3-540-77355-9 (softcover)",
LCCN = "QA448.D38 I577 2006",
MRclass = "68-06 (03B35 51-06 68T15 68U05)",
MRnumber = "2866844 (2012h:68002)",
bibdate = "Thu May 22 15:42:50 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/lncs2007a.bib",
note = "Revised papers from the 6th International Workshop
(ADG 2006) held at the University of Vigo, Pontevedra,
August 31--September 2, 2006",
series = "Lecture Notes in Computer Science",
abstract = "This book constitutes the thoroughly refereed
post-proceedings of the 6th International Workshop on
Automated Deduction in Geometry, ADG 2006, held at
Pontevedra, Spain, in August/September 2006 as a
satellite event of the International Congress of
Mathematicians, ICM 2006. The 13 revised full papers
presented were carefully selected from the submissions
made due to a call for papers - within the scope of ADG
shortly after the meeting. The papers show the lively
variety of topics and methods and the current
applicability of automated deduction in geometry to
different branches of mathematics and to other sciences
and technologies.",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
}
@Proceedings{Furbach:2007:ART,
editor = "Ulrich Furbach and Natarajan Shankar",
booktitle = "{Automated Reasoning: Third International Joint
Conference, IJCAR 2006, Seattle, WA, USA, August
17--20, 2006: Proceedings}",
title = "{Automated Reasoning: Third International Joint
Conference, IJCAR 2006, Seattle, WA, USA, August
17--20, 2006: Proceedings}",
volume = "4130",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 680",
year = "2007",
ISBN = "3-540-37187-7 (paperback), 3-540-37188-5 (e-book)",
ISBN-13 = "978-3-540-37187-8 (paperback), 978-3-540-37188-5
(e-book)",
LCCN = "QA76.9.A96 I33 2006",
bibdate = "Thu May 22 15:32:05 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/lncs2007a.bib",
series = "Lecture Notes in Computer Science Ser.",
URL = "http://WX7CF7ZP2H.search.serialssolutions.com/?V=1.0&L=WX7CF7ZP2H&S=JCs&C=TC",
abstract = "Here are the proceedings of the Third International
Joint Conference on Automated Reasoning, IJCAR 2006,
held in Seattle, Washington, USA, August 2006. The book
presents 41 revised full research papers and 8 revised
system descriptions, with 3 invited papers and a
summary of a systems competition. The papers are
organized in topical sections on proofs, search,
higher-order logic, proof theory, proof checking,
combination, decision procedures, CASC-J3, rewriting,
and description logic.",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
subject = "Automatic theorem proving; Artificial intelligence",
}
@Proceedings{IEEE:2007:ISV,
editor = "IEEE",
booktitle = "{4th International Symposium on Voronoi Diagrams in
Science and Engineering (ISVD 2007): School of
Computing, University of Glamorgan, Pontypprid, Wales,
UK}",
title = "{4th International Symposium on Voronoi Diagrams in
Science and Engineering (ISVD 2007): School of
Computing, University of Glamorgan, Pontypprid, Wales,
UK}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2007",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Aug 13 18:49:38 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Stutzle:2007:ESL,
editor = "Thomas St{\"u}tzle and Mauro Birattari and Holger H.
Hoos",
booktitle = "{Engineering Stochastic Local Search Algorithms.
Designing, Implementing and Analyzing Effective
Heuristics, International Workshop, SLS 2007, Brussels,
Belgium, September 6--8, 2007, Proceedings}",
title = "{Engineering Stochastic Local Search Algorithms.
Designing, Implementing and Analyzing Effective
Heuristics, International Workshop, SLS 2007, Brussels,
Belgium, September 6--8, 2007, Proceedings}",
volume = "4638",
publisher = pub-SV,
address = pub-SV:adr,
year = "2007",
ISBN = "3-540-74445-2",
ISBN-13 = "978-3-540-74445-0",
bibdate = "Thu Aug 13 18:38:32 2009",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/sls/sls2007.html;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Book{Gavrilova:2008:GVD,
editor = "Marina L. Gavrilova",
booktitle = "Generalized {Voronoi} diagram: a geometry-based
approach to computational intelligence",
title = "Generalized {Voronoi} diagram: a geometry-based
approach to computational intelligence",
volume = "158",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxi + 312",
year = "2008",
DOI = "https://doi.org/10.1007/978-3-540-85126-4",
ISBN = "3-540-85126-7, 3-540-85125-9",
ISBN-13 = "978-3-540-85126-4, 978-3-540-85125-7",
ISSN = "1860-949X",
LCCN = "QA278.2 .G46 2008ebeb; QA278.2 .G46 2008eb; QA278.2;
QA278.2 .G46 2008",
bibdate = "Thu Aug 13 18:45:14 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
melvyl.cdlib.org:210/CDL90",
series = "Studies in computational intelligence",
acknowledgement = ack-nhfb,
subject = "Voronoi polygons; Computational intelligence",
}
@Book{Kao:2008:EA,
editor = "Ming-Yang Kao",
booktitle = "Encyclopedia of algorithms",
title = "Encyclopedia of algorithms",
publisher = pub-SV,
address = pub-SV:adr,
pages = "liii + 1166",
year = "2008",
DOI = "https://doi.org/10.1007/978-0-387-30162-4",
ISBN = "0-387-30162-3, 0-387-30770-2",
ISBN-13 = "978-0-387-30162-4, 978-0-387-30770-1",
LCCN = "QA9.58 .E52 2007eb; QA9.58 .E52 2007ebeb; QA9.58;
QA9.58 .E52 2007",
bibdate = "Thu Aug 13 18:40:37 MDT 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
melvyl.cdlib.org:210/CDL90",
series = "Springer reference",
acknowledgement = ack-nhfb,
subject = "Computer algorithms; Encyclopedias; Algorithms",
}
@Proceedings{Fukuda:2010:MSI,
editor = "Komei Fukuda and Joris {Van der Hoeven} and Michael
Joswig and Nobuki Takayama",
booktitle = "{Mathematical Software --- ICMS 2010: Third
International Congress on Mathematical Software, Kobe,
Japan, September 13--17, 2010, Proceedings}",
title = "{Mathematical Software --- ICMS 2010: Third
International Congress on Mathematical Software, Kobe,
Japan, September 13--17, 2010, Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 368",
year = "2010",
ISBN = "3-642-15581-2 (paperback)",
ISBN-13 = "978-3-642-15581-9 (paperback)",
LCCN = "QA76.95 .I5654 2010",
bibdate = "Thu May 22 16:13:39 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Lecture Notes in Computer Science / Theoretical
Computer Science and General Issues Ser.",
URL = "http://link.springer.com/openurl?genre=book&isbn=978-3-642-15581-9",
abstract = "This book constitutes the refereed proceedings of the
Third International Congress on Mathematical Software,
ICMS 2010, held in Kobe, Japan in September 2010. The
49 revised full papers presented were carefully
reviewed and selected for presentation. The papers are
organized in topical sections on computational group
theory, computation of special functions, computer
algebra and reliable computing, computer tools for
mathematical editing and scientific visualization,
exact numeric computation for algebraic and geometric
computation, formal proof, geometry and visualization,
Groebner bases and applications, number theoretical
software as well as software for optimization and
polyhedral computation.",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
meetingname = "International Congress of Mathematical Software (3rd :
2010 : K{\=o}be-shi, Japan)",
subject = "Mathematics; Data processing; Congresses; Computer
software; Computer software.; Data processing.",
}
@Book{Lagarias:2011:KCH,
editor = "Jeffrey C. Lagarias",
booktitle = "The {Kepler Conjecture}: the {Hales--Ferguson} proof
by {Thomas C. Hales} and {Samuel P. Ferguson}",
title = "The {Kepler Conjecture}: the {Hales--Ferguson} proof
by {Thomas C. Hales} and {Samuel P. Ferguson}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 456",
year = "2011",
ISBN = "1-4614-1128-9 (paperback), 1-4614-1129-7 (e-book)",
ISBN-13 = "978-1-4614-1128-4 (paperback), 978-1-4614-1129-1
(e-book)",
LCCN = "QA166.7 .K47 2011",
bibdate = "Wed Jan 9 08:09:14 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/kepler.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "Samuel P. Ferguson; Thomas C. Hales",
remark = "Includes a special issue of \booktitle{Discrete and
Computational Geometry}.",
subject = "Kepler's conjecture",
tableofcontents = "Part 1. Introduction and survey \\
Chapter 1. The Kepler Conjecture and Its Proof / J. C.
Lagarias / 3--26 \\
Chapter 2. Bounds for Local Density of Sphere Packings
and the Kepler Conjecture / J. C. Lagarias / 27--61 \\
Part 2. Proof of the Kepler Conjecture \\
Chapter 3. Historical Overview of the Kepler Conjecture
/ T. C. Hales / 65--82 \\
Chapter 4. A Formulation of the Kepler Conjecture / T.
C. Hales and S. P. Ferguson / 83--134 \\
Chapter 5. Sphere Packings III. Extremal Cases / T. C.
Hales / 135--173 \\
Chapter 6. Sphere Packings IV. Detailed Bounds / T. C.
Hales / 177--234 \\
Chapter 7. Sphere Packings V. Pentahedral Prisms / S.
P. Ferguson / 235--274 \\
Chapter 8. Sphere Packings VI. Tame Graphs and Linear
Programs / T. C. Hales / 275--340 \\
Part 3. A revision to the proof of the Kepler
conjecture \\
Chapter 9. A Revision of the Proof of the Kepler
Conjecture / T. C. Hales, J. Harrison, S. McLaughlin,
T. Nipkow, S. Obua; R. Zumkeller / 341--378 \\
Part 4. Initial papers of the Hales program \\
Chapter 10. Sphere Packings I / T. C. Hales / 379--432
\\
Chapter 11. Sphere Packings II / T. C. Hales / 433--450
\\
Index of Symbols / 451--452 \\
Index of Subjects / 453--456",
}
@Proceedings{Carette:2013:ICM,
editor = "Jacques Carette and David Aspinall and Christoph Lange
and Petr Sojka and Wolfgang Windsteiger",
booktitle = "{Intelligent computer mathematics: MKM, Calculemus,
DML, and Systems and Projects 2013, held as part of
CICM 2013, Bath, UK, July 8--12, 2013. Proceedings}",
title = "{Intelligent computer mathematics: MKM, Calculemus,
DML, and Systems and Projects 2013, held as part of
CICM 2013, Bath, UK, July 8--12, 2013. Proceedings}",
volume = "7961",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 384",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-39320-4",
ISBN = "3-642-39319-5 (paperback), 3-642-39320-9 (e-book)",
ISBN-13 = "978-3-642-39319-8 (paperback), 978-3-642-39320-4
(e-book)",
LCCN = "QA76.9.M35 I58 2013",
bibdate = "Thu May 22 15:57:56 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/kepler.bib;
http://www.math.utah.edu/pub/tex/bib/lncs2013a.bib",
series = "Lecture notes in computer science",
acknowledgement = ack-nhfb,
keywords = "Project Flyspeck",
subject = "Informatique; Math{\'e}matiques; Congr{\`e}s;
Intelligence artificielle; Computer science; Algebra;
Data processing; Information storage and retrieval
systems; Artificial intelligence; Text processing
(Computer science)",
tableofcontents = "Calculemus: The rooster and the butterflies / Assia
Mahboubi \\
Optimising Problem Formulation for Cylindrical
Algebraic Decomposition / Russell Bradford, James H.
Davenport, Matthew England, and David Wilson \\
The Formalization of Syntax-Based Mathematical
Algorithms Using Quotation and Evaluation / William M.
Farmer \\
Certification of bounds of non-linear functions: the
templates method / Xavier Allamigeon, St{\'e}phane
Gaubert, Victor Magron, and Benjamin Werner \\
Verifying a Platform for Digital Imaging: A Multi-tool
Strategy / Jonathan Heras, Gadea Mata, Ana Romero,
Julio Rubio, and Rub{\'e}n S{\'a}enz \\
A Universal Machine for Biform Theory Graphs / Michael
Kohlhase, Felix Manse and Florian Rabe \\
MKM: Mathematical Practice, Crowdsourcing, and Social
Machines / Ursula Martin and Alison Pease \\
Automated Reasoning Service for HOL Light / Cezary
Kaliszyk and Josef Urban \\
Understanding Branch Cuts of Expressions / Matthew
England, Russell Bradford, James H. Davenport, and
David Wilson \\
Formal Mathematics on Display: A Wiki for Flyspeck /
Carst Tankink, Cezary Kaliszyk, Josef Urban, and Herman
Geuvers \\
Determining Points on Handwritten Mathematical Symbols
/ Rui Hu and Stephen M. Watt \\
Capturing Hiproofs in HOL Light / Steven Obua, Mark
Adams, and David Aspinall \\
A Qualitative Comparison of the Suitability of Four
Theorem Provers for Basic Auction Theory / Christoph
Lange, Marco B. Caminati, Manfred Kerber, Till
Mossakowski, Colin Rowat, Makarius Wenzel, and Wolfgang
Windsteiger \\
Students' Comparison of Their Trigonometric Answers
with the Answers of a Computer Algebra System / Eno
Tonisson \\
DML: Mathematics and the World Wide Web / Patrick D.F.
Ion \\
Structural Similarity Search for Mathematics Retrieval
/ Shahab Kamali and Frank Wm. Tompa \\
Towards Machine-Actionable Modules of a Digital
Mathematics Library: The Example of DML-CZ / Michal
R{\^e}u\?zi\?cka, Petr Sojka, and Vlastimil Krej\?c\c
\?r \\
A Hybrid Approach for Semantic Enrichment of MathML
Mathematical Expressions / Minh-Quoc Nghiem, Giovanni
Yoko Kristianto, Goran Topi{\'c}, and Akiko Aizawa \\
Three Years of DLMF: Web, Math and Search / Bruce R.
Miller \\
Escaping the Trap of Too Precise Topic Queries / Paul
Libbrecht \\
Using MathML to Represent Units of Measurement for
Improved Ontology Alignment / Chau Do and Eric J.
Pauwels \\
Systems and projects: A Web Interface for Isabelle: The
Next Generation / Christoph L{\"u}th and Martin Ring
\\
The ForMaRE Project--Formal Mathematical Reasoning in
Economics / Christoph Lange, Colin Rowat, and Manfred
Kerber \\
LATExml 2012--A Year of LATExml / Deyan Ginev and Bruce
R. Miller \\
The MMT API: A Generic MKM System / Florian Rabe \\
Math-Net.Ru as a Digital Archive of the Russian
Mathematical Knowledge from the XIX Century to Today /
Dmitry E. Chebukov, Alexander D. Izaak, Olga G.
Misyurina, Yuri A. Pupyrev, and Alexey B. Zhizhchenko
\\
A Dynamic Symbolic Geometry Environment Based on the
Gr{\"o}bnerCover Algorithm for the Computation of
Geometric Loci and Envelopes / Miguel A. Ab{\'a}nades
and Francisco Botana \\
ML4PG in computer algebra verification / J{\'o}nathan
Heras and Ekaterina Komendantskaya \\
Pervasive Parallelism in Highly-Trustable Interactive
Theorem Proving Systems / Bruno Barras, Lourdes del
Carmen Gonz{\'a}lez Huesca, Hugo Herbelin, Yann
R{\'e}gis-Gianas, Enrico Tassi, Makarius Wenzel, and
Burkhart Wolff \\
The Web geometry laboratory project / Pedro Quaresma,
Vanda Santos, and Seifeddine Bouallegue \\
swMATH--A New Information Service for Mathematical
Software / Sebastian B{\"o}bisch, Michael Brickenstein,
Hagen Chrapary, Gert-Martin Greuel, and Wolfram Sperber
\\
Software for evaluating relevance of steps in algebraic
transformations / Rein Prank \\
The DeLiverMATH project: text analysis in mathematics /
Ulf Sch{\"o}nberg and Wolfram Sperber",
xxseries = "Lecture notes in artificial intelligence; LNCS
sublibrary. SL 7, Artificial intelligence",
}
@Proceedings{Hong:2014:MSI,
editor = "Hoon Hong and Chee-Keng Yap",
booktitle = "{Mathematical Software --- ICMS 2014: 4th
International Conference, Seoul, South Korea, August
5--9, 2014. Proceedings}",
title = "{Mathematical Software --- ICMS 2014: 4th
International Conference, Seoul, South Korea, August
5--9, 2014. Proceedings}",
volume = "8592",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxi + 735",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2",
ISBN = "3-662-44198-5, 3-662-44199-3 (e-book)",
ISBN-13 = "978-3-662-44198-5, 978-3-662-44199-2 (e-book)",
LCCN = "QA76.95",
bibdate = "Sat Aug 13 13:49:23 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
series = "Lecture Notes in Computer Science",
abstract = "This book constitutes the proceedings of the 4th
International Conference on Mathematical Software, ICMS
2014, held in Seoul, South Korea, in August 2014. The
108 papers included in this volume were carefully
reviewed and selected from 150 submissions. The papers
are organized in topical sections named: invited;
exploration; group; coding; topology; algebraic;
geometry; surfaces; reasoning; special; Gr{\"o}bner;
triangular; parametric; interfaces and general.",
acknowledgement = ack-nhfb,
subject = "Mathematik.; Software.",
tableofcontents = "Experimental Computation and Visual Theorems \\
Soft Math --- Math Soft \\
Flyspecking Flyspeck \\
Symbolic Computing Package for Mathematica for
Versatile Manipulation of Mathematical Expressions \\
Representing, Archiving, and Searching the Space of
Mathematical Knowledge \\
Early Examples of Software in Mathematical Knowledge
Management \\
Discourse-Level Parallel Markup and Meaning Adoption in
Flexiformal Theory Graphs \\
Complexity Analysis of the Bivariate Buchberger
Algorithm in Theorema \\
Theorema 2.0: A System for Mathematical Theory
Exploration \\
New Approaches in Black Box Group Theory \\
A GAP Package for Computing with Real Semisimple Lie
Algebras \\
Bacterial Genomics and Computational Group Theory: The
BioGAP Package for GAP \\
SgpDec: Cascade (De)Compositions of Finite
Transformation Semigroups and Permutation Groups \\
Approximating Generators for Integral Arithmetic Groups
\\
Software for Groups: Theory and Practice \\
Computation of Genus 0 Belyi Functions \\
On Computation of the First Baues-Wirsching Cohomology
of a Freely-Generated Small Category \\
Codes over a Non Chain Ring with Some Applications \\
On the Weight Enumerators of the Projections of the
2-adic Golay Code of Length 24 to Z2e \\
Computer Based Reconstruction of Binary Extremal
Self-dual Codes of Length 32 \\
Magma Implementation of Decoding Algorithms for General
Algebraic Geometry Codes \\
Reversible Codes and Applications to DNA \\
javaPlex: A Research Software Package for Persistent
(Co)Homology \\
PHAT \\
Persistent Homology Algorithms Toolbox \\
Computing Persistence Modules on Commutative Ladders of
Finite Type \\
Heuristics for Sphere Recognition \\
CAPD::RedHom v2 \\
Homology Software Based on Reduction Algorithms \\
The Gudhi Library: Simplicial Complexes and Persistent
Homology \\
Bertini real: Software for One- and Two-Dimensional
Real Algebraic Sets \\
Hom4PS-3: A Parallel Numerical Solver for Systems of
Polynomial Equations Based on Polyhedral Homotopy
Continuation Methods \\
Geometry CGAL \\
Reliable Geometric Computing for Academia and Industry
\\
Implementing the L[infinity] Segment Voronoi Diagram in
CGAL and Applying in VLSI Pattern Analysis \\
BULL! \\
The Molecular Geometry Engine Based on Voronoi Diagram,
Quasi-Triangulation, and Beta-Complex \\
Integrating Circumradius and Area Formulae for Cyclic
Pentagons \\
Computer Aided Geometry \\
The Sustainability of Digital Educational Resources \\
A Touch-Operation-Based Dynamic Geometry System: Design
and Implementation \\
OpenGeo: An Open Geometric Knowledge Base \\
On Computing a Cell Decomposition of a Real Surface
Containing Infinitely Many Singularities \\
Robustly and Efficiently Computing Algebraic Curves and
Surfaces \\
Computing the Orthogonal Projection of Rational Curves
onto Rational Parameterized Surface by Symbolic Methods
\\
Isotopic Approximation of Algebraic Curves \\
Isotopic Arrangement of Simple Curves: An Exact
Numerical Approach Based on Subdivision \\
Real Quantifier Elimination in the RegularChains
Library \\
Software for Quantifier Elimination in Propositional
Logic \\
Quantifier Elimination for Linear Modular Constraints
\\
Skolemization Modulo Theories \\
Incremental QBF Solving by DepQBF \\
NLCertify: A Tool for Formal Nonlinear Optimization \\
Developing Linear Algebra Packages on Risa/Asir for
Eigenproblems \\
Mathematical Software for Modified Bessel Functions \\
BetaSCP2: A Program for the Optimal Prediction of
Side-Chains in Proteins \\
Computation of an Improved Lower Bound to Giuga's
Primality Conjecture \\
An Extension and Efficient Calculation of the Horner's
Rule for Matrices \\
What Is New in CoCoA? \\
Maximizing Likelihood Function for Parameter Estimation
in Point Clouds via Gr{\"o}bner Basis \\
Gr{\"o}bner Basis in Geodesy and Geoinformatics \\
Gr{\"o}bner Bases in Theorema \\
Effective Computation of Radical of Ideals and Its
Application to Invariant Theory \\
Generic and Parallel Gr{\"o}bner Bases in JAS \\
Application of Gr{\"o}bner Basis Methodology to
Nonlinear Mechanics Problems \\
Software for Discussing Parametric Polynomial Systems:
The Gr{\"o}bner Cover \\
An Algorithm for Computing Standard Bases by Change of
Ordering via Algebraic Local Cohomology \\
Verification of Gr{\"o}bner Basis Candidates \\
Cylindrical Algebraic Decomposition in the
RegularChains Library \\
Hierarchical Comprehensive Triangular Decomposition \\
A Package for Parametric Matrix Computations \\
Choosing a Variable Ordering for Truth-Table Invariant
Cylindrical Algebraic Decomposition by Incremental
Triangular Decomposition \\
Using the Regular Chains Library to Build Cylindrical
Algebraic Decompositions by Projecting and Lifting \\
An Improvement of Rosenfeld-Gr{\"o}bner Algorithm \\
Doing Algebraic Geometry with the RegularChains Library
\\
On Multivariate Birkhoff Rational Interpolation \\
Computing Moore-Penrose Inverses of Ore Polynomial
Matrices \\
Software Using the Gr{\"o}bner Cover for Geometrical
Loci Computation and Classification \\
Using Maple's RegularChains Library to Automatically
Classify Plane Geometric Loci \\
Solving Parametric Polynomial Systems by
RealComprehensiveTriangularize \\
QE Software Based on Comprehensive Gr{\"o}bner Systems
\\
SyNRAC: A Tolbox for Solving Real Algebraic
Constraints.-An Algorithm for Computing Tjurina
Stratifications of [mu]-Constant Deformations by Using
Local Cohomology Classes with Parameters \\
An Implementation Method of Boolean Gr{\"o}bner Bases
and Comprehensive Boolean Gr{\"o}bner Bases on General
Computer Algebra Systems \\
A Method to Determine if Two Parametric Polynomial
Systems Are Equal \\
An Implementation Method of a CAS with a Handwriting
Interface on Tablet Devices \\
New Way of Explanation of the Stochastic Interpretation
of Wave Functions and Its Teaching Materials Using
KETpic \\
IFSGen4LATEX: Interactive Graphical User Interface For
Generation and Visualization of Iterated Function
Systems in LATEX \\
GNU TEXMACS Towards a Scientific Office Suite \\
Computer Software Program for Representation and
Visualization of Free-Form Curves through Bio-inspired
Optimization Techniques \\
On Some Attempts to Verify the Effect of Using
High-Quality Graphics in Mathematics Education \\
Math Web Search Interfaces and the Generation Gap of
Mathematicians \\
Practice with Computer Algebra Systems in Mathematics
Education and Teacher Training Courses \\
Development of Visual Aid Materials in Teaching the
Bivariate Normal Distributions \\
Creating Interactive Graphics for Mathematics Education
Utilizing KETpic \\
A Tablet-Compatible Web-Interface for Mathematical
Collaboration \\
Development and Evaluation of a Web-Based Drill System
to Master Basic Math Formulae Using a New Interactive
Math Input Method \\
Generating Data of Mathematical Figures for 3D Printers
with KETpic and Educational Impact of the Printed
Models \\
A Touch-Based Mathematical Expression Editor \\
Establishment of KETpic Programming Styles for Drawing
\\
Integration of Libnormaliz in CoCoALib and CoCoA 5 \\
Elements of Design for Containers and Solutions in the
LinBox Library \\
Recent Developments in Normaliz \\
The Basic Polynomial Algebra Subprograms \\
Function Interval Arithmetic \\
Generating Optimized Sparse Matrix Vector Product over
Finite Fields \\
swMATH \\
An Information Service for Mathematical Software \\
MathLibre: Modifiable Desktop Environment for
Mathematics \\
Software Packages for Holonomic Gradient Method \\
Metalibm: A Mathematical Functions Code Generator \\
From Calculus to Algorithms without Errors \\
Dense Arithmetic over Finite Fields with the CUMODP
Library",
}