Chow polynomials of uniform matroids are real-rooted

Abstract

June Huh and Matthew Stevens conjectured that the Hilbert-Poincaré series of the Chow ring of any matroid is a polynomial with only real zeros. We prove this conjecture for the class of uniform matroids. We also prove that the Chow polynomial and the augmented Chow polynomial of any maximally ranked poset has only real zeros.

9 pages, 1 figure version 2: minor changes and added Corollary 4.2