FUNCTION: NcsfMat - transition matrix from X-basis to Y-basis

CALLING SEQUENCE:

NcsfMat(n,X,Y)

NCSF[NcsfMat](n,X,Y)

PARAMETERS:

X,Y = two bases

n = any positive integer (n>0)

SYNOPSIS:

• The NcsfMat function computes the transition matrix from the X-basis to the Y-basis.

• In noncommutative theory, we defined following bases: L-basis : noncommutative elementary symmetric functions, Ph-basis : noncommutative power sums symmetric functions of the second kind, Ps-basis : noncommutative power sums symmetric functions of the first kind, R-basis : ribbon Schur functions, S-basis : noncommutative complete symmetric functions.

• The result is a 2^(n-1) x 2^(n-1) square matrix.

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

EXAMPLES:

> with(NCSF):
> NcsfMat(3,'R','S');
 
                               [  1   0   0  0 ]
                               [               ]
                               [ -1   1   0  0 ]
                               [               ]
                               [ -1   0   1  0 ]
                               [               ]
                               [  1  -1  -1  1 ]