FUNCTION: CompPerm - compare two permutations

CALLING SEQUENCE:

CompPerm(perm_1, perm_2, kind)

SG[CompPerm](perm_1, perm_2, kind)

PARAMETERS:

perm_1, perm_2 = any lists denoting permutations

kind = 'lexic', 'cixel', 'bruhat'

SYNOPSIS:

• The CompPerm function compares two permutations. The ordering is set by the argument kind, and the function returns true if perm_1 >= perm_2 according to the choosen ordering.

• kind='lexic' for lexicographic ordering.

• kind='cixel' for inverse lexicographic ordering that is lexicographic ordering from right to left.

• kind='bruhat' to compare the two permutations according to the Bruhat order.

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

EXAMPLES:

> with(SG):
> CompPerm([3,1,2], [1,3,2], 'lexic');
 
                                      true
 
> CompPerm([3,1,2], [1,3,2], 'cixel');
 
                                     false
 
> CompPerm([3,1,2], [1,3,2], 'bruhat');
 
                                      true