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    Growth diagrams, Domino insertion and Sign-imbalance

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    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.Comment: 24 page

    The uncrossing partial order on matchings is Eulerian

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    We prove that the partial order on the set of matchings of 2n points on a circle, given by resolving crossings, is an Eulerian poset.Comment: 6 page
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