Descent Statistics for Hyperoctahedral Groups

Ron M Adin, Francesco Brenti and Yuval Roichman

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


Three new statistics on the hyperoctahedral group $B_{n}$ are introduced. It is shown that they give two generalizations of Carlitz's identity for the descent number and major index over $S_{n}$. This answers a question posed by Foata. These statistics are then extended to a family of refined ``descent statistics", leading to multivariate identities.

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