FUNCTION: PermOnCTab - action of a permutation on a product of columns

CALLING SEQUENCE:

PermOnCTab(perm, ctab)

TAB[PermOnCTab](perm, ctab)

PARAMETERS:

perm = any list denoting a permutation

ctab = any list of lists denoting a product of columns

SYNOPSIS:

• The PermOnCTab function plactically permutes columns in a product of columns ctab (not necessarily a contre-tableau, but obtained from a contretableau by permutation).

• A simple plactic column-transposition transforms a two-column contre- tableau into the two-column tableau which is obtained from it by Schensted algorithm, or conversely. This transformation is also given by the jeu de taquin.

• When used with the extra argument 'nil', it nilplactically permutes columns, exchanging for instance [[1], [2,1]] and [[2,1], [2]], while a plactic column-transposition exchanges [[1], [2,1]] with [[2,1], [1]]. Whenever the contretableau is not a reduced decomposition, it returns [].

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

EXAMPLES:

> with(TAB):
> PermOnCTab([2,1], [[5], [6,2], [7,4,3,1]]);
 
                       [[5, 2], [6], [7, 4, 3, 1]]
 
> PermOnCTab([2,1], [[3], [4,3]], 'nil');
 
                                [[4, 3], [4]]