FUNCTION: Perm2Rise - compute the list of rises of a permutation

CALLING SEQUENCE:

Perm2Rise(perm)

SG[Perm2Rise](perm)

PARAMETERS:

perm = any list denoting a permutation

SYNOPSIS:

• The Perm2Rise function computes the list of rises 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 rises of the permutation perm.

• When called with the second argument 'rin', it returns the sum of the rise positions (rise index).

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

• Whenever there is a conflict between the function name Perm2Rise and another name used in the same session, use the long form SG['Perm2Rise'].

EXAMPLES:

> with(SG):
> perm:=[3,1,4,2,6,5,7,8]:
> Perm2Rise(perm);
 
                                 [2, 4, 6, 7]
 
> Perm2Rise(perm, 'nb');
 
                                      4
 
> Perm2Rise(perm, 'rin');
 
                                      9
 
> Perm2Rise(perm, 'corin');
 
                                      13