FUNCTION: Word2CTab - convert a word into a contretableau

CALLING SEQUENCE:

Word2CTab(w)

TAB[Word2CTab](w)

PARAMETERS:

w = any word

SYNOPSIS:

• The Word2Tab function inserts a word [x1, x2, ...] into an empty contre- tableau from the right. It first inserts x1, then x2, and so on.

• The insertion algorithm is due to Schensted.

• When called with the 'nil' option as second argument, the Word2CTab function nilplactically inserts the word into the empty contretableau. Whenever the word is not a reduced decomposition, it returns [].

• Whenever there is a conflict between the function name Word2CTab and another name used in the same session, use the long form TAB['Word2CTab'].

EXAMPLES:

> with(TAB):
> CTab2Mat( Word2CTab(w[5,6,2,4,3,7,1]) );
 
                                 [ 5  6  7 ]
                                 [         ]
                                 [    2  4 ]
                                 [         ]
                                 [       3 ]
                                 [         ]
                                 [       1 ]
 
> Word2CTab(w[1,2,1,3,2,1], 'nil');
 
                           [[1], [2, 1], [3, 2, 1]]