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Descent Numbers and Major Indices for the Hyperoctahedral Group

Ron M. Adin·Francesco Brenti·Yuval Roichman
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Abstract

We introduce and study three new statistics on the hyperoctahedral group $B_{n}$, and show 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.

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Ron M. Adin, Francesco Brenti, Yuval Roichman. 2000-12-14. Descent Numbers and Major Indices for the Hyperoctahedral Group. https://arxiv.org/abs/math/0012111

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