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Descent numbers and major indices for the hyperoctahedral group. (English) Zbl 0995.05008

Authors’ abstract (extended): We introduce and study three new statistics on the hyperoctahedral group \(B_n\) and show that they give two generalizations of L. Carlitz’s identity [A combinatorial property of \(q\)-Eulerian numbers, Am. Math. Mon. 82, 51-54 (1975; Zbl 0296.05007)] for the descent number and major index over \(S_n\). This answers a question posed by D. Foata [personal communication, July 2000]: extend the (“Euler-Mahonian”) bivariate distribution of descent number and major idex to the hyperoctahedral group \(B_n\).

MSC:

05A15 Exact enumeration problems, generating functions
20F55 Reflection and Coxeter groups (group-theoretic aspects)

Citations:

Zbl 0296.05007
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References:

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