Abstracts
for the Seminar

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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