• Korean Journal of Mathematics
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• v.24 no.3
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• pp.469-487
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• 2016

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.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.445-459
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• 1998

Let λ be a partition with all distinct parts. In this paper we give a bijection between the set $\Gamma$$_{λ}$(X) of pairs (equation omitted) satisfying a certain condition and the set $\pi_{λ}$(X) of circled permutation tableaux of shape λ on the set X, where P$\frac{1}{2}$ is a tail circled shifted rim hook tableaux of shape λ and (equation omitted) is a barred permutation on X. Specializing to the partition λ with one part, this bijection gives a combinatorial proof of the Schur identity: $\Sigma$2$\ell$(type($\sigma$)) = 2n! summed over all permutation $\sigma$ $\in$ $S_{n}$ with type($\sigma$) $\in$ O $P_{n}$ . .