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SYMF::SfJtMat -- computes the Jacobi-Trudi matrix

Call(s)


SYMF::SfJtMat(part <,b>)

Parameters

part- any list denoting a (skew) partition
b- any name

Introduction

The SYMF::SfJtMat function computes the Jacobi-Trudi matrix corresponding to the (skew) partition part. The determinant of this matrix is exactly the Schur function indexed by the partition, expressed in the h-basis.

When given a second argument, b, SYMF::SfJtMat returns a result expressed on the b-basis.

Example 1

>> muEC::SYMF::SfJtMat( [3,2,1,1] );
                       +-                        -+
                       |  h[3], h[4], h[5], h[6]  |
                       |                          |
                       |  h[1], h[2], h[3], h[4]  |
                       |                          |
                       |    0,    1,  h[1], h[2]  |
                       |                          |
                       |    0,    0,    1,  h[1]  |
                       +-                        -+
>> muEC::SYMF::SfJtMat( [[2,1], [1]] );
                             +-            -+
                             |  h[1], h[3]  |
                             |              |
                             |    0,  h[1]  |
                             +-            -+
>> muEC::SYMF::SfJtMat( [[2,2,1], [1,1,1]], b );
                          +-                  -+
                          |  b[1], b[2], b[3]  |
                          |                    |
                          |    1,  b[1], b[2]  |
                          |                    |
                          |    0,    0,    1   |
                          +-                  -+

Related Functions

Iss

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MuPAD Combinat, an open source algebraic combinatorics package