FUNCTION: NcsfPlethysm - computes the plethysm of symmetric function and a quasi-symmetric function

CALLING SEQUENCE:

NcsfPlethysm(sf,qsf)

NcsfPlethysm(sf,qsf)

NCSF[NcsfPlethysm](sf,qsf)

NCSF[NcsfPlethysm](sf,qsf)

PARAMETERS:

sf = any symmetric function

qsf = any quasi-symmetric function

SYNOPSIS:

• The NcsfPlethysm function computes the plethysm of a symmetric function and a quasi-symmetric function. The plethysm is defined by: NcsfPlethysm(pk,M[i1,..,ir]) = M[k*i1,...k*ir]

• sf is any expression in terms of the basic symmetric functions.

• qsf is any expression in terms of the basic quasi-symmetric functions.

• The sf and the qsf functions are expanded and the result is not collected.

• One may add 'noexpand' just after the argument qsf to choose not to expand sf and qsf before treating it.

• One may collect the result by adding an argument: this is done by NcsfPlethysm(sf,qsf,'collect').

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

EXAMPLES:

> with(NCSF):
> NcsfPlethysm((1+q)^3*s[2,1],M[1,1]):         #         expands the input
> NcsfPlethysm((1+q)^3*s[2,1],M[1,1],noexpand):#   does not expand (1+q)^3
> NcsfPlethysm((1+q)^5*s[2,1],M[1,1],collect): #       collects the result
> NcsfPlethysm((1-q)^3*s[1,1],M[1,1],noexpand,collect);
 
                      3                         3
           - (- 1 + q)  M[1, 2, 1] - 3 (- 1 + q)  M[1, 1, 1, 1]
 
                          3                       3
               - (- 1 + q)  M[1, 1, 2] - (- 1 + q)  M[2, 1, 1]