THE JEU DE TAQUIN ON THE SHIFTED RIM HOOK TABLEAUX

The Schensted algorithm first described by Robinson [5] is a remarkable combinatorial correspondence associated with the theory of symmetric functions. $Sch{\ddot{u}}tzenberger jeu de taquin[10] can be used to give alternative descriptions of both P- and Q-tableaux of the Schensted algorithm as well as the ordinary and dual Knuth relations. In this paper we describe the jeu de taquin on shifted rim hook tableaux using the switching rule, which shows that the sum of the weights of the shifted rim hook tableaux of a given shape and content does not depend on the order of the content if content parts are all odd.