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


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.


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

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A. Berele, A Schensted-type correspondence for the symplectic group, J. Combin. Theory Ser. A 43 (1986), 320–328. (Google Scholar)

D. E. Knuth, Sorting and Searching; The Art of Computer Programming, Vol. 3 (1973), Addison-Wesley, Mass. (Google Scholar)

D. E. Knuth, Permutations, matrices, and generalized Young tableaux, Pacific J. Math. 34 (1970), 709–727. (Google Scholar)

J. Lee, A Schensted algorithm for shifted rim hook tableaux, J. Korean Math. Soc. 31 (1994), 179–203. (Google Scholar)

B. E. Sagan, Shifted tableaux, Schur Q-functions and a conjecture of R. Stanley, J. Combin. Theory Ser. A 45 (1987), 62–103. (Google Scholar)

C. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961), 179–191. (Google Scholar)

B. Sagan and R. Stanley, Robinson-Schensted algorithms for skew tableaux, J. Combin. Theory Ser. A 55 (1990), 161–193. (Google Scholar)

D. W. Stanton and D. E. White, A Schensted algorithm for rim hook tableaux, J. Combin. Theory Ser. A 40 (1985), 211–247. (Google Scholar)

D. E. White, A bijection proving orthogonality of the characters of Sn, Advances in Math. 50 (1983), 160–186. (Google Scholar)

D. R. Worley, A Theory of Shifted Young Tableaux, Ph. D. thesis (1984), M.I.T. (Google Scholar)


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