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## `PART::SkewPart2Mat` -- a planar representation of a skew partition

#### Call(s)

`PART::SkewPart2Mat(skp <,alphabet=l>)`

#### Parameters

`skp` | - | a skew part

#### Options

`alphabet=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

#### Introduction

The `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 Functions

`ListSkewDiag`, `Part2Mat`, `TYP::IsSkewDiag`, `TYP::IsSkewPart`

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MuPAD Combinat, an open source algebraic combinatorics package