PART::ListSkewDiag
--
list of skew diagrams
PART::ListSkewDiag(n <,options>)
n | - | any non negative integer |
maxlg=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.
The 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.
>> 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
ListPart
, ListPartIn
, SkewPart2Mat
, TYP::IsSkewDiag
, TYP::IsSkewPart
MuPAD Combinat, an open source algebraic combinatorics package