Journal of Combinatorics

Volume 10 (2019)

Number 4

Special Issue in Memory of Jeff Remmel, Part 2 of 2

Guest Editor: Nicholas A. Loehr

A polyhedral proof of a wreath product identity

Pages: 711 – 723

DOI: https://dx.doi.org/10.4310/JOC.2019.v10.n4.a5

Authors

Robert Davis (Harvey Mudd College, Claremont, California, U.S.A.)

Bruce Sagan (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)

Abstract

In 2013, Beck and Braun proved and generalized multiple identities involving permutation statistics via discrete geometry. Namely, they recognized the identities as specializations of integer point transform identities for certain polyhedral cones. They extended many of their proof techniques to obtain identities involving wreath products, but some identities were resistant to their proof attempts. In this article, we provide a geometric justification of one of these wreath product identities, which was first established by Biagioli and Zeng.

Keywords

descent set, generating function, major index, polytope, wreath product

Full Text (PDF format)

This paper is dedicated to the memory of Jeff Remmel. It concerns two mathematical objects which he studied over his long and productive research career: permutation statistics and wreath products.

Received 7 December 2017

Published 17 July 2019