FUNCTION: RandPerm - return a random permutation

CALLING SEQUENCE:

RandPerm(n)

RandPerm(n, typeperm)

SG[RandPerm](n)

SG[RandPerm](n, typeperm)

PARAMETERS:

n = any positive integer denoting the degree of a symmetric group

typeperm = 'dominant', 'grassmannian'

SYNOPSIS:

• The RandPerm function generates a random permutation belonging to the symmetric group of degree n.

• RandPerm(n, 'dominant') returns a random dominant permutation.

• RandPerm(n, 'grassmannian') returns a random grassmannian permutation.

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

EXAMPLES:

> with(SG):
> RandPerm(7);
 
                             [7, 4, 2, 3, 5, 1, 6]
 
> r := RandPerm(20, 'dominant');
 
      r := [15, 11, 10, 12, 13, 7, 6, 8, 9, 14, 16, 5, 4, 17, 3, 18, 2,
 
            19, 20, 1]
 
> Perm2Code(r);
 
       [14, 10, 9, 9, 9, 6, 5, 5, 5, 5, 5, 4, 3, 3, 2, 2, 1, 1, 1, 0]