FUNCTION: SfJtMat - compute the Jacobi-Trudi matrix

CALLING SEQUENCE:

SfJtMat(part)

SYMF[SfJtMat](part)

PARAMETERS:

part = any list denoting a (skew) partition

SYNOPSIS:

• The 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.

• Whenever one uses a second argument b, the entries of the matrix are the bi's instead of the hi's.

• Whenever there is a conflict between the function name SfJtMat and another name used in the same session, use the long form SYMF['SfJtMat'].

EXAMPLES:

> with(SYMF):
> SfJtMat([3,2,1,1]);
 
                               [ h3  h4  h5  h6 ]
                               [                ]
                               [ h1  h2  h3  h4 ]
                               [                ]
                               [  0   1  h1  h2 ]
                               [                ]
                               [  0   0   1  h1 ]
 
> SfJtMat([[2,1], [1]]);
 
                                   [ h1  h3 ]
                                   [        ]
                                   [  0  h1 ]
 
> SfJtMat([[2,2,1], [1,1,1]], 'b');
 
                                 [ b1  b2  b3 ]
                                 [            ]
                                 [  1  b1  b2 ]
                                 [            ]
                                 [  0   0   1 ]