  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.
