FUNCTION: Perm2Betti - compute the Betti polynomial

CALLING SEQUENCE:

Perm2Betti(perm, 'q')

SG[Perm2Betti](perm, 'q')

PARAMETERS:

perm = any list denoting any permutation

SYNOPSIS:

• The Perm2Betti function computes the generating function of the lengths of all permutations that are smaller than a given permutation perm, according to Bruhat order.

• The second parameter 'q' can be arbitrarily choosen.

• Whenever there is a conflict between the function name Perm2Betti and another name used in the same session, use the long form SG['Perm2Betti'].

EXAMPLES:

> with(SG):
> Perm2Betti([3,4,1,2], 'q');
 
                            4      3      2
                           q  + 4 q  + 5 q  + 3 q + 1