The Eulerian distribution on the involutions of the hyperoctahedral group is unimodal

The Eulerian distribution on the involutions of the symmetric group is unimodal, as shown by Guo and Zeng. In this paper we prove that the Eulerian distribution on the involutions of the hyperoctahedral group, when viewed as a colored permutation group, is unimodal in a similar way and we compute its generating function, using signed quasisymmetric functions.Comment: 11 pages, zero figure

Growth diagrams, Domino insertion and Sign-imbalance

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

Combinatorial Gelfand Models

A combinatorial construction of a Gelafand model for the symmetric group and its Iwahori-Hecke algebra is presented.Comment: 15 pages, revised version, to appear in J. Algebr