ar X iv : q - a lg / 9 70 90 10 v 1 4 S ep 1 99 7 August 7 , 1997 DOMINO TABLEAUX , SCHÜTZENBERGER INVOLUTION , AND THE SYMMETRIC GROUP ACTION

Abstract

We define an action of the symmetric group S[ n 2 ] on the set of domino tableaux, and prove that the number of domino tableaux of weight β does not depend on the permutation of the weight β. A bijective proof of the well-known result due to J. Stembridge that the number of self–evacuating tableaux of a given shape and weight β = (β1, . . . , β[ n+1 2 ], β[ n2 ], . . . , β1), is equal to that of domino tableaux of the same shape and weight β = (β1, . . . , β[ n+1 2 ]) is given.

Cite this paper

@inproceedings{Kirillov2009arXI, title={ar X iv : q - a lg / 9 70 90 10 v 1 4 S ep 1 99 7 August 7 , 1997 DOMINO TABLEAUX , SCH{\"{U}TZENBERGER INVOLUTION , AND THE SYMMETRIC GROUP ACTION}, author={Anatol N. Kirillov}, year={2009} }