## The Homogenized Linial Arrangement and Genocchi Numbers

- Oct. 18, 2019
- 2:30 p.m.

## Abstract

In this talk, I will present joint work with Michelle Wachs in which we use a different method to refine and extend Hetyei's results. We study the intersection lattice of this hyperplane arrangement and give a combinatorial interpretation of the coefficients of its characteristic polynomial. This approach leads to new combinatorial models for the Genocchi and median Genocchi numbers, and to a generating function formula for the characteristic polynomial that reduces to generating functions of Barsky and Dumont for the Genocchi and median Genocchi numbers. We also study type B and complex hyperplane analogs of the homogenized Linial arrangement, and are able to extend many of our results to these settings.