PART::ListSkewDiag --
list of skew diagrams
Call(s)
PART::ListSkewDiag(n <,options>)
Parametersn | - | any non negative integer |
Optionsmaxlg=l | - | maximum length of skew diagrams |
mininner=p | - | minimal inner partition |
maxinner=p | - | maximal inner partition |
minouter=p | - | minimal outer partition |
maxouter=p | - | maximal outer partition |
nb | - | only counts objects |
Use the syntax hold(identifier), instead of
identifier, if one of the identifiers above is already
defined.
IntroductionThe PART::ListSkewDiag function gives all skew diagrams of n.
Skew diagrams are special cases of skew partitions.
A skew partition of n is a list of two partitions
part1 and part2 such that
part1 is greater than part2
(with respect to inclusion of diagrams) and n equals
wght(part1) - wght(part2), where
wght() is the weight function.
By skew diagrams, we mean skew partitions where empty columns and empty rows have been erased.
When called with one argument, say n, the function returns
the list of all skew diagrams of n.
The outer partition corresponds to the outer shape of the skew diagram and the inner partition corresponds to the inner shape of the skew diagram.
Given a skew diagram skd,
_plus(op(op(skd,1)))-_plus(op(op(skd,2))) gives its
weight.
Example 1>> muEC::PART::ListSkewDiag( 2 );
[[[2], []], [[2, 1], [1]], [[1, 1], []]]
>> muEC::PART::ListSkewDiag( 3, mininner=[1], maxouter=[3,1,1] );
[[[3, 1], [1]], [[2, 1, 1], [1]]]
>> muEC::PART::ListSkewDiag( 3, maxinner=[1], minouter=[3] );
[[[3], []], [[3, 1], [1]]]
>> muEC::PART::ListSkewDiag( 10, maxlg=5, nb );
5309
Related FunctionsListPart, ListPartIn, SkewPart2Mat, TYP::IsSkewDiag, TYP::IsSkewPart
MuPAD Combinat, an open source algebraic combinatorics package