Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture
Combinatorics
2021-10-12 v2
Abstract
We give a short proof of the log-concavity of the coefficients of the reduced characteristic polynomial of a matroid. The proof uses an extension of the theory of Lorentzian polynomials to convex cones, and reproves the Hodge-Riemann relations of degree one for the Chow ring of a matroid.
Keywords
Cite
@article{arxiv.2110.00487,
title = {Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture},
author = {Petter Brändén and Jonathan Leake},
journal= {arXiv preprint arXiv:2110.00487},
year = {2021}
}