Shifted tableaux, schur Q-functions, and a conjecture of R. Stanley

Abstract 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. Combin. Theory Ser. A 27 (1979) , 10–18]. 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 Knuth's construction ( Pacific J. Math. 34 (1970) , 709–727). The fact that the Knuth relations hold for our algorithm yields a simple proof of a conjecture of Stanley.

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