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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.
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참고문헌 (10)
참고문헌 신청
A. Berele / 1986 / A Schensted-type correspondence for the symplectic group / J. Combin. Theory Ser. A 43:320~328
D. E. Knuth / 1973 / Sorting and Searching; The Art of Computer Programming, Vol. 3 / Addison-Wesley
D. E. Knuth / 1970 / Permutations, matrices, and generalized Young tableaux / Pacific J. Math 34:709~727
J. Lee / 1994 / A Schensted algorithm for shifted rim hook tableaux / J. Korean Math. Soc 31:179~203
B. E. Sagan / 1987 / Shifted tableaux, Schur Q-functions and a conjecture of R. Stanley / J. Combin. Theory Ser. A 45:62~103
D. E. Knuth / 1973 / Sorting and Searching; The Art of Computer Programming, Vol. 3 / Addison-Wesley
D. E. Knuth / 1970 / Permutations, matrices, and generalized Young tableaux / Pacific J. Math 34:709~727
J. Lee / 1994 / A Schensted algorithm for shifted rim hook tableaux / J. Korean Math. Soc 31:179~203
B. E. Sagan / 1987 / Shifted tableaux, Schur Q-functions and a conjecture of R. Stanley / J. Combin. Theory Ser. A 45:62~103
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