FUNCTION: Perm2ListInv - calculate the set of inversions of a permutation

CALLING SEQUENCE:

Perm2ListInv(perm)

SG[Perm2ListInv](perm)

PARAMETERS:

perm = any list denoting a permutation

SYNOPSIS:

• The Perm2ListInv function calculates the list of all inversions of a permutation. The result is in lexicographic ordering.

• The set of inversions is a set of pairs of positions (i,j) such that i<j and perm[j]<perm[i].

• Whenever there is a conflict between the function name Perm2ListInv and another name used in the same session, use the long form SG['Perm2ListInv'].

EXAMPLES:

> with(SG):
> Perm2ListInv(Perm2Inv([4,1,3,2]));
 
                       [{1, 4}, {2, 3}, {2, 4}, {3, 4}]
 
> Perm2ListInv([4,1,3,2]);
 
                      [{1, 2}, {1, 3}, {1, 4}, {3, 4}]