FUNCTION: Schensted - Schensted correspondence

CALLING SEQUENCE:

Schensted(w)

TAB[Schensted](w)

PARAMETERS:

w = any word

SYNOPSIS:

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

• When used with a second parameter 'nil', the first tableau in the result is a nil-plactic tableau.

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

EXAMPLES:

> with(TAB):
> sch:=Schensted(w[4,1,2,4,2]);
 
             sch := [[[4, 4], [1, 2, 2]], [[2, 5], [1, 3, 4]]]
 
> map(Tab2Mat, sch);
 
                         [ 4  4    ]  [ 2  5    ]
                        [[         ], [         ]]
                         [ 1  2  2 ]  [ 1  3  4 ]
 
> Schensted(w[4,5,1,2,3,1], 'nil');
 
             [[[4], [2, 5], [1, 2, 3]], [[6], [3, 4], [1, 2, 5]]]