PART::SkewPart2Mat --
a planar representation of a skew partition
Call(s)
PART::SkewPart2Mat(skp <,alphabet=l>)
Parametersskp | - | a skew part |
Optionsalphabet=l | - | l is a list of 1 to 3 components,
l[1] filling the skew diagram,
l[2] the inner diagram and
l[3] the outside |
IntroductionThe PART::SkewPart2Mat function gives a planar representation of a skew
partition in the Cartesian plane, i.e. the north-east quadrant.
A skew partition is a list of two partitions p1 and
p2 such that p1 is greater than p2 (with
respect to inclusion of diagrams).
Example 1>> muEC::PART::SkewPart2Mat( [[3,2],[2]] );
+- -+
| 1, 1, 0 |
| |
| 0, 0, 1 |
+- -+
>> print(Unquoted, muEC::PART::SkewPart2Mat( [[3,2],[2]], alphabet=["#",".",""] )):
+- -+
| #, #, |
| |
| ., ., # |
+- -+
>> map( muEC::PART::ListSkewDiag(3),muEC::PART::SkewPart2Mat )
-- +- -+
| +- -+ +- -+ | 1, 0, 0 |
| +- -+ | 1, 0, 0 | | 1, 1, 0 | | |
| | 1, 1, 1 |, | |, | |, | 0, 1, 0 |,
| +- -+ | 0, 1, 1 | | 0, 0, 1 | | |
| +- -+ +- -+ | 0, 0, 1 |
-- +- -+
+- -+ +- -+ +- -+ --
+- -+ +- -+ | 1, 0 | | 1, 0 | | 1 | |
| 1, 0 | | 1, 1 | | | | | | | |
| |, | |, | 0, 1 |, | 1, 0 |, | 1 | |
| 1, 1 | | 0, 1 | | | | | | | |
+- -+ +- -+ | 0, 1 | | 0, 1 | | 1 | |
+- -+ +- -+ +- -+ --
Related FunctionsListSkewDiag, Part2Mat, TYP::IsSkewDiag, TYP::IsSkewPart
MuPAD Combinat, an open source algebraic combinatorics package