FUNCTION: InvSchensted - inverse Schensted correspondence

CALLING SEQUENCE:

InvSchensted(pair)

InvSchensted(pair, 'left')

InvSchensted(pair, 'nil')

TAB[InvSchensted](pair)

TAB[InvSchensted](pair, 'left')

TAB[InvSchensted](pair, 'nil')

PARAMETERS:

pair = any list of one tableau and one standard tableau

SYNOPSIS:

• The InvSchensted function gives the bijection between pairs of tableaux and words. The argument pair is a list of two tableaux of the same shape, the second one being standard and called the (right) insertion tableau. The result is the word corresponding to this pair of tableaux.

• When called with a second argument 'left', the standard tableau is the left insertion tableau.

• When called with a second argument 'nil', the first tableau is a nil-plactic tableau.

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

EXAMPLES:

> with(TAB):
> r := Schensted(w[1,4,2,4,2]);
 
             r := [[[4, 4], [1, 2, 2]], [[3, 5], [1, 2, 4]]]
 
> InvSchensted(r);
 
                              w[1, 4, 2, 4, 2]
 
> InvSchensted(r, 'left');
 
                              w[4, 1, 4, 2, 2]
 
> InvSchensted([[[4],[2,5],[1,2,3]], [[6],[3,4],[1,2,5]]], 'nil');
 
                             w[4, 5, 1, 2, 3, 1]