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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