• 대한수학회지
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• 제56권4호
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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.

• Korean Journal of Mathematics
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• 제21권3호
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• pp.223-236
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• 2013

Schensted algorithm was first described in 1938 by Robinson [5], in a paper dealing with an attempt to prove the correctness of the Littlewood-Richardson rule. Schensted [9] rediscovered Schensted algorithm independently in 1961 and Viennot [12] gave a geometric interpretation for Schensted algorithm in 1977. In this paper we describe some properties of Schensted algorithm using Viennot's geometric interpretation.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.469-487
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• 2016

In [6] Schensted constructed the Schensted algorithm, which gives a bijection between permutations and pairs of standard tableaux of the same shape. Stanton and White [8] gave analog of the Schensted algorithm for rim hook tableaux. In this paper we give a generalization of Stanton and White's Schensted algorithm for rim hook tableaux. If k is a fixed positive integer, it shows a one-to-one correspondence between all generalized hook permutations $\mathcal{H}$ of size k and all pairs (P, Q), where P and Q are semistandard k-rim hook tableaux and k-rim hook tableaux of the same shape, respectively.

• Korean Journal of Mathematics
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• 제23권3호
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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.