Korean J. Math.  Vol 23, No 3 (2015)  pp.427-438
DOI: https://doi.org/10.11568/kjm.2015.23.3.427

The jeu de taquin on the shifted rim hook tableaux

Jaejin Lee

Abstract


The Schensted algorithm first described by Robinson [5] is a remarkable combinatorial correspondence associated with the theory of symmetric functions. Sch\"{u}tzenberger's 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.

Keywords


partition, shifted rim hook tableau, Schensted algorithm, switching rule, jeu de taquin.

Subject classification

05E10.

Sponsor(s)



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References


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