Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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GENERALIZATION OF THE SCHENSTED ALGORITHM FOR RIM HOOK TABLEAUX

  • Received : 2016.07.04
  • Accepted : 2016.09.01
  • Published : 2016.09.30
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Abstract

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.

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References

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