Descent Numbers and Major Indices for the Hyperoctahedral Group

Authors:
Ron M. Adin;Francesco Brenti;Yuval Roichman
Affiliations:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israelf1radin@math.biu.ac.ilf1;Dipartimento di Matematica, Universitá di Roma Tor Vergata Via della Ricerca Scientifica, 00133, Rome, Italyf2brenti@mat.uniroma2.itf2;Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israelf3yuvalr@math.biu.ac.ilf3
Venue:
Advances in Applied Mathematics
Year:
2001

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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.