Generalization of the Schensted algorithm for rim hook tableaux
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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.
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.
참고문헌 (10)
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- D. W. Stanton, "A Schensted algorithm for rim hook tableaux", J. Combin. Theory Ser. A, 40, pp.211~247 (1985)
- D. E. White, "A bijection proving orthogonality of the characters of Sn", Advances in Math, 50, pp.160~186 (1983)
- D. R. Worley, "A Theory of Shifted Young Tableaux", Ph. D., pp.1984