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

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.