FUNCTION: Perm2Desc - compute the list of descents of a permutation

CALLING SEQUENCE:

Perm2Desc(perm)

SG[Perm2Desc](perm)

PARAMETERS:

perm = any list denoting a permutation

SYNOPSIS:

• The Perm2Desc function computes the list of descents of the permutation perm, i.e. the list of positions i, such that perm[i] > perm[i+1].

• When called with the second argument 'nb', it returns the number of descents of the permutation perm.

• When called with the second argument 'maj', it returns the sum of the descent positions.

• When called with the second argument 'comaj', it returns the sum of all values (n - descent position), where n is equal to nops(perm).

• Whenever there is a conflict between the function name Perm2Desc and and another name used in the same session, use the long form SG['Perm2Desc'].

EXAMPLES:

> with(SG):
> perm:=[3,1,4,2,6,5,7]:
> Perm2Desc(perm);
 
                                  [1, 3, 5]
 
> Perm2Desc(perm, 'nb');
 
                                      3
 
> Perm2Desc(perm, 'maj');
 
                                      9
 
> Perm2Desc(perm, 'comaj');
 
                                      12