FUNCTION: Free2PlaxClass - replace each word by its plactic class

CALLING SEQUENCE:

Free2PlaxClass(free)

FREE[Free2PlaxClass](free)

PARAMETERS:

free = any element of the free algebra

SYNOPSIS:

• The Free2PlaxClass function replaces each word by the sum of all words which are in the same plactic class (i.e. which give the same tableau by Schensted algorithm).

• Whenever there is a conflict between the function name Free2PlaxClass and another name used in the same session, use the long form FREE['Free2PlaxClass'].

EXAMPLES:

> with(FREE):
> Free2PlaxClass(w[2,3,1,3]);
 
                w[2, 1, 3, 3] + w[2, 3, 1, 3] + w[2, 3, 3, 1]
 
> Free2PlaxClass(q*w[2,3,1] + w[2,1,3]);
 
                   (1 + q) w[2, 3, 1] + (1 + q) w[2, 1, 3]