FUNCTION: ListYama - generate all Yamanouchi words of a given evaluation

CALLING SEQUENCE:

ListYama(part)

TAB[ListYama](part)

PARAMETERS:

part = any list denoting a partition

SYNOPSIS:

• The ListYama function computes all Yamanouchi words (also called "lattice permutations") corresponding to a given partition part. By default, it lists left Yamanouchi words. Left and right Yamanouchi words code standard tableaux.

• ListYama(part) = ListYama(part, 'left') but one can also list all right Yamanouchi words of a given evaluation by using ListYama(part, 'right').

• Right Yamanouchi words are exactly the words which are plactically congruent to the word ...3^part[3] 2^part[2] 1^part[1] or, equivalently, give the tableau [..., [3...3], [2...2], [1...1]] by Schensted algorithm. They are in bijection with their right insertion tableau.

• Left and right Yamanouchi words are exchanged when reading words from right to left.

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

EXAMPLES:

> with(TAB):
> ListYama([2,1], 'right');
 
                           [w[1, 2, 1], w[2, 1, 1]]
 
> ListYama([3,2]);
 
            [w[1, 2, 1, 2, 1], w[1, 2, 1, 1, 2], w[1, 1, 2, 1, 2],
 
                      w[1, 1, 1, 2, 2], w[1, 1, 2, 2, 1]]