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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