Ron M. Adin, Francesco Brenti, Yuval Roichman
Published 2000-12-14Version 1
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.
On some analogues of Carlitz's identity for the hyperoctahedral group
The poset of Specht ideals for hyperoctahedral groups
Orbits of the hyperoctahedral group as Euclidean designs
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