• Korean Journal of Mathematics
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• v.21 no.3
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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.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.901-914
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• 1999

In [6] Schensted constructed the Schensted algorithm giving a bijection between permutations and pairs of Young standard tableaux. After knuth generalized it to column strict tableaux in [3] various analogs of the Schensted algorithm came. In this paper we describe the bumping algorithm on the shifted rim hook tableaux which is the basic building block of the Schensted algorithm for shifted rim book tableaux.

• Korean Journal of Mathematics
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• v.24 no.3
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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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• v.14 no.1
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• pp.125-136
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• 2006

Using the Bumping algorithm for the shifted rim hook tableaux described in [5], we construct Schensted insertion and deletion algorithms for shifted rim hook tableaux. This may give us the combinatorial proof for the orthogonality of the second kind of the spin characters of $S_n$.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.445-453
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• 2007

Using Schensted Insertion and Deletion algorithm for shifted rim hook tableaux described in [7], we construct Schensted algorithm for shifted rim hook tableaux. This give us the combinatorial proof for the orthogonality of the second kind for the spin characters of $\tilde{S}n$.

• 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.31 no.2
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• pp.179-203
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• 1994