Korean J. Math.  Vol 24, No 3 (2016)  pp.469-487
DOI: https://doi.org/10.11568/kjm.2016.24.3.469

Generalization of the Schensted algorithm for rim hook tableaux

Jaejin Lee

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.

Keywords


partition, hook, rim hook, generalized hook permutation, rim hook tableau, semistandard rim hook tableau, Schensted algorithm

Subject classification

05E10

Sponsor(s)



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References


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