FUNCTION: Perm2Length - calculate the length of a permutation

CALLING SEQUENCE:

Perm2Length(perm)

SG[Perm2Length](perm)

PARAMETERS:

perm = any list denoting a permutation

SYNOPSIS:

• The Perm2Length function calculates the length of the permutation perm, that is its number of inversions. This is also the minimal length of an expression of the permutation as a product of simple transpositions, as well as the sum of the components of its code.

• Whenever there is a conflict between the function name Perm2Length and another name used in the same session, use the long form SG['Perm2Length'].

EXAMPLES:

> with(SG):
> perm:=[5,3,2,1,4]:
> Perm2Length(perm);
 
                                       7
 
> Perm2Rd(perm);
 
                              [4, 3, 2, 1, 3, 2, 3]
 
> Perm2Code(perm);
                                [4, 2, 1, 0, 0]