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PART::ListSkewDiag -- list of skew diagrams

Call(s)


PART::ListSkewDiag(n <,options>)

Parameters

n- any non negative integer

Options

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.

Introduction

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.

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 Functions

ListPart, ListPartIn, SkewPart2Mat, TYP::IsSkewDiag, TYP::IsSkewPart

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MuPAD Combinat, an open source algebraic combinatorics package