FUNCTION: Perm2Interval - compute all codes of permutations below a given one

CALLING SEQUENCE:

Perm2Interval(perm)

SG[Perm2Interval](perm)

PARAMETERS:

perm = any list denoting a permutation

SYNOPSIS:

• The Perm2Interval function computes the list of the Lehmer codes of all permutations that are smaller than perm, according to the Bruhat order.

• Whenever there is a conflict between the function name Perm2Interval and another name used in the same session, use the long form SG['Perm2Interval'].

EXAMPLES:

> with(SG):
> Perm2Interval([3,1,2]);
 
                  [[2, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0]]
 
> map(Code2Perm, Perm2Interval([3,2,1]));
 
      [[3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 3, 2], [1, 2, 3]]