Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Fall 2022

Speaker:  Jose Bastidas, Université du Québec à Montréal
Title: The Primitive Eulerian polynomial
Time: 2:30 PM, Monday, October 24, 2022
Place:  Malott 206

Abstract: We introduce the Primitive Eulerian polynomial $P_{\mathcal{A}}(z)$ of a central hyperplane arrangement $\mathcal{A}$, a reparametrization of its cocharacteristic polynomial. Previous work on the polytope algebra of deformations of a zonotope (2021) implicitly showed that this polynomial has nonnegative coefficients whenever $\mathcal{A}$ is a simplicial arrangement, but a combinatorial interpretation of the coefficients was only found for reflection arrangements of type A and B. We discuss the relationship between the Primitive Eulerian polynomial and the usual Eulerian polynomial. We also present a geometric/combinatorial interpretation for the coefficients of $P_{\mathcal{A}}(z)$ for all simplicial arrangements $\mathcal{A}$, along with some real-rootedness results and conjectures. Based on joint work with Christophe Hohlweg and Franco Saliola.

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