Penn Arts & Sciences Logo

CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, February 7, 2013 - 2:00pm

Mirko Visontai

KTH

Location

University of Pennsylvania

DRL 3C6

The MacMahon--Carlitz q-analog of the Eulerian polynomial is a two-variable generating function of the joint distribution of descent and the major index statistic over permutations, $A_n(x,q) = \sum_\pi x^\des\pi q^\maj\pi$. In this talk, we first prove a conjecture of Chow and Gessel that asserts that the zeros of these q-Eulerian polynomials are all real and are "logarithmically spaced", in the sense that the ratio of the consecutive zeros is at least $q$ (for $q>1$). The proof is then extended to signed permutations and is also used to settle a more general conjecture of Chow and Mansour for the case of colored permutations. This is joint work with Petter Brändèn and Matthew Chasse.