Growth diagrams, domino insertion and sign-imbalance

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:107

Article

Lam, T

关键词: young tableaux;    domino tableaux;    growth diagrams;    domino insertion;    sign imbalance;    Robinson-Schensted algorithm;    symmetric functions;   

DOI  :  10.1016/j.jcta.2004.03.010

来源: Elsevier

【 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.

【 授权许可】

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