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Growth diagrams, Domino insertion and Sign-imbalance

Thomas Lam
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Abstract

We study some properties of domino insertion, focusing on aspects related to Fomin's growth diagrams. We give a self-contained proof of the semistandard domino-Schensted correspondence given by Shimozono and White, bypassing the connections with mixed insertion entirely. The correspondence is extended to the case of a nonempty 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 and to generalise the domino generating series of Kirillov, Lascoux, Leclerc and Thibon.

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Thomas Lam. 2003-08-27. Growth diagrams, Domino insertion and Sign-imbalance. https://arxiv.org/abs/math/0308265

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