FUNCTION: Sf2Free - from symmetric polynomials to words

CALLING SEQUENCE:

Sf2Free(sf, n)

FREE[Sf2Free](sf, n)

PARAMETERS:

sf = any symmetric polynomial

n = any nonnegative integer denoting the number of variables

SYNOPSIS:

• The Sf2Free function converts a symmetric polynomial sf in n variables into an element of the free algebra. The correspondance amounts to develop each Schur function as a sum of tableaux (seen as special words) of a given shape. Thus, the symmetric function is first expressed in the basis of Schur functions and then each Schur function is converted.

• Whenever there is a conflict between the function name Sf2Free and another name used in the same session, use the long form FREE['Sf2Free'].

EXAMPLES:

> with(FREE):
> Sf2Free(e3, 4);
 
             w[3, 2, 1] + w[4, 2, 1] + w[4, 3, 1] + w[4, 3, 2]
 
> Sf2Free(s[2,1], 3);
 
             w[2, 1, 1] + w[3, 1, 1] + w[2, 1, 2] + w[3, 1, 2]
 
           + w[2, 1, 3] + w[3, 1, 3] + w[3, 2, 2] + w[3, 2, 3]