• Korean Journal of Mathematics
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• v.23 no.3
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• pp.427-438
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• 2015

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

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.947-984
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• 2019

We provide two shifted analogues of the tableau switching process due to Benkart, Sottile, and Stroomer; the shifted tableau switching process and the modified shifted tableau switching process. They are performed by applying a sequence of elementary transformations called switches and shares many nice properties with the tableau switching process. For instance, the maps induced from these algorithms are involutive and behave very nicely with respect to the lattice property. We also introduce shifted generalized evacuation which exactly agrees with the shifted J-operation due to Worley when applied to shifted Young tableaux of normal shape. Finally, as an application, we give combinatorial interpretations of Schur P- and Schur Q-function related identities.