Séminaire Lotharingien de Combinatoire, B61Ak (2010), 13 pp.

Riccardo Biagioli and Jiang Zeng

On Some Analogues of Descent Numbers and Major Index for the Hyperoctahedral Group

Abstract. We give a new description of the flag major index, introduced by Adin and Roichman, by using a major index defined by Reiner. This allows us to establish a connection between an identity of Reiner and some more recent results due to Chow and Gessel. Furthermore we generalize the main identity of Chow and Gessel by computing the four-variate generating series of descents, major index, length, and number of negative entries over Coxeter groups of type B and D.

Received: September 23, 2009. Accepted: October 5, 2010. Final Version: October 18, 2010.

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