FUNCTION: Word2Tab - convert a word into a tableau

CALLING SEQUENCE:

Word2Tab(w)

TAB[Word2Tab](w)

PARAMETERS:

w = any word

SYNOPSIS:

• The Word2Tab function inserts a word [x1, x2, ...] into an empty 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 Word2Tab function nilplactically inserts the word into the empty tableau. Whenever the word is not a reduced decomposition, it returns [].

• Whenever there is a conflict between the function name Word2Tab and another name used in the same session, use the long form TAB['Word2Tab'].

EXAMPLES:

> with(TAB):
> Tab2Mat( Word2Tab(w[5,6,2,4,3,7,1]) );
 
                                 [ 5       ]
                                 [         ]
                                 [ 4       ]
                                 [         ]
                                 [ 2  6    ]
                                 [         ]
                                 [ 1  3  7 ]
 
> Word2Tab(w[1,2,1,3,2,1], 'nil');
 
                          [[3], [2, 3], [1, 2, 3]]