FUNCTION: GenPerm - generate an element of the symmetric group

CALLING SEQUENCE:

GenPerm(n, typeperm)

GenPerm(perm, typeperm)

SG[GenPerm](n, typeperm)

SG[GenPerm](perm, typeperm)

PARAMETERS:

n = any positive integer

perm = any list denoting a permutation

typeperm = 'first', 'previous', 'next', 'last'

SYNOPSIS:

• The GenPerm function generates one element of a symmetric group in lexicographic order, according to the parameter typeperm.

• GenPerm(n, 'first') returns the first permutation of S(n).

• GenPerm(n, 'last') returns the last permutation of S(n).

• GenPerm(perm, 'previous') gives the previous permutation according to the lexicographic order. It returns the NULL value when perm is already the first permutation.

• GenPerm(perm, 'next') gives the next permutation according to the lexicographic order. It returns the NULL value when perm is already the last permutation.

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

EXAMPLES:

> with(SG):
> GenPerm([3, 1, 4, 2], 'next');
 
                                [3, 2, 1, 4]
> GenPerm([3, 2, 1, 4], 'previous');
 
                                [3, 1, 4, 2]