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Descent Numbers and Major Indices for the Hyperoctahedral Group

✍ Scribed by Ron M. Adin; Francesco Brenti; Yuval Roichman

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 137 KB
Volume: 27
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0731

No coin nor oath required. For personal study only.

✦ Synopsis

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.  2001 Elsevier Science

1. Introduction

A well known classical result due to MacMahon (see ) asserts that the inversion number and major index of a permutation are equidistributed

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