SYMMETRICA-MANUAL -- Jeu de taquin, Lehmer code

Jeu de taquin, Lehmer code

Jeu de taquin, Lehmer code

A very interesting routine is the inverse jeu de taquin. You enter an arbitrary tableau and a coordinate at its right border, and now you can apply the inverse jeu de taquin. The result is a tableau with an entry at the starting point and a new free place at the left border.

NAME: inverse_jeudetaquin_tableaux
SYNOPSIS:

INT inverse_jeudetaquin_tableaux(OP ta; INT i,j; OP erg)

As there the plactic and nilplactic relations you can play the jeu de taquin with the nilplactic relations,too:

NAME: inverse_nilplactic_jeudetaquin_tableaux
SYNOPSIS:

INT inverse_nilplactic_jeudetaquin_tableaux (OP t; INT i,j; OP e)

To each permutation, defined, say, by its Lehmer code, there corresponds a reduced decomposition.

NAME: lehmercode_tableaux
SYNOPSIS: INT lehmercode_tableaux(OP a,b)
DESCRIPTION: computes a LIST b of tableaux, which are reduced decomposition of the permutation perm, given by the Lehmer code a.

harald.fripertinger "at" uni-graz.at, May 26, 2011

Jeu de taquin, Lehmer code