FUNCTION: BumpC - insert a word into a contretableau

CALLING SEQUENCE:

BumpC(ct, w)

TAB[BumpC](ct, w)

PARAMETERS:

ct = any list of list(s) denoting a contretableau

w = any word

SYNOPSIS:

• The BumpC function inserts a word [x1, x2, ...] into a contretableau 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 third argument, the BumpC function nilplactically inserts the word into the contretableau from the right.

• The nilplactic insertion algorithm makes BumpC([], w[1,2,1], 'nil') to BumpC([], w[2,1,2], 'nil'). Whenever the result of the insertion is not a reduced decomposition, it returns [].

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

EXAMPLES:

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