Growth diagrams, domino insertion and sign-imbalance

We study some properties of domino insertion, focusing on aspects related to Fomin’s growth diagrams [Fom1, Fom2]. We give a self-contained proof of the semistandard domino-Schensted correspondence given by Shimozono and White [SW], 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’ conjecture on signimbalance [Sta] and to generalise the domino generating series of Kirillov, Lascoux, Leclerc and Thibon [KLLT] .