• Honam Mathematical Journal
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• v.26 no.3
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• pp.257-268
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• 2004

In this paper, we give a proof of the Robinson-Schensted-Knuth correspondence by using the geometric. construction. We represent a generalized permutation in the first quadrant of the Cartesian plane and find a corresponding pair of semi-standard tableaux of same shape. This work extends the classical geometric construction of Viennot [10] for Robinson-Schensted correspondence.

• 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.