Growth diagrams, domino insertion and sign-imbalance

摘要

We study some properties of domino insertion, focusing on aspects related to Fomin's growth diagrams (J. Algebraic Combin. 3 (1994) 357; J. Algebraic Conibin. 4 (1995) 5). We give a self-contained proof of the semistandard domino-Schensted correspondence given by Shimozono and White (Electron. J. Combin. 8 (2001)), bypassing the connections with mixed insertion entirely. The correspondence is extended to the case of a non-empty 2-core and we give two dual domino-Schensted correspondences. We use our results to settle Stanley's '2(n/2), conjecture on sign-imbalance (preprint, math. CO/021111 3, 2002) and to generalise the domino generating series of Kirillov et al. (C.R. Acad. Sci. Paris, Serie I 318 (1994) 395). (C) 2004 Elsevier Inc. All rights reserved.