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Shifted tableaux, Schur q-functions, and a conjecture of R. Stanley. (English) Zbl 0661.05010
We present an analog of the Robinson-Schensted correspondence that applies to shifted Young tableaux and is considerably simpler than the one proposed in [B. E. Sagan, J. Comb. Theory, Ser. A 27, 10-18 (1979; Zbl 0428.05005)]. In addition, this algorithm enjoys many of the important properties of the original Robinson-Schensted map including an interpretation of row lengths in terms of k-increasing sequences, a jeu de taquin, and a generalization to tableaux with repeated entries analogous to D. E. Knuth’s construction [Pac. J. Math. 34, 709-727 (1970; Zbl 0199.319)]. The fact that the Knuth relations hold for our algorithm yields a simple proof of a conjecture of Stanley.

MSC:
05A17 Combinatorial aspects of partitions of integers
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