Chow polynomials of uniform matroids are real-rooted
Combinatorics
2025-09-19 v2
Abstract
June Huh and Matthew Stevens conjectured that the Hilbert-Poincar\'e 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.
Cite
@article{arxiv.2501.07364,
title = {Chow polynomials of uniform matroids are real-rooted},
author = {Petter Brändén and Lorenzo Vecchi},
journal= {arXiv preprint arXiv:2501.07364},
year = {2025}
}
Comments
9 pages, 1 figure version 2: minor changes and added Corollary 4.2