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

CALLING SEQUENCE:

QsfMat(n,X,Y)

NCSF[QsfMat](n,X,Y)

PARAMETERS:

X,Y = two bases

n = any positive integer (n>0)

SYNOPSIS:

• The QsfMat function computes the transition matrix from the X-basis to the Y-basis, where X and Y being bases of quasi-symetric functions.

• In quasi-symmetric theory, we defined following bases: E-basis : elementary quasi-symmetric functions, QPh-basis : dual basis of noncommutative power sums symmetric functions of the second kind, QPs-basis : dual basis of noncommutative power sums symmetric functions of the first kind, F-basis : ribbon Schur quasi-symmetric function M-basis : monomial quasi-symmetric functions.

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

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

EXAMPLES:

> with(NCSF):
> QsfMat(3,'F','M');
 
                                 [ 1  1  1  1 ]
                                 [            ]
                                 [ 0  1  0  1 ]
                                 [            ]
                                 [ 0  0  1  1 ]
                                 [            ]
                                 [ 0  0  0  1 ]