Three results related to the half-plane property of matroids
Combinatorics
2026-01-30 v1
Abstract
We settle three problems from the literature on stable and real zero polynomials and their connection to matroid theory. We disprove the weak real zero amalgamation conjecture by Schweighofer and the second author. We disprove a conjecture by Br\"and\'en and D'Le\'on by finding a relaxation of a matroid with the weak half-plane property that does not have the weak half-plane property itself. Finally, we prove that every quaternionic unimodular matroid has the half-plane property which was conjectured by Pendavingh and van Zwam.
Keywords
Cite
@article{arxiv.2402.01272,
title = {Three results related to the half-plane property of matroids},
author = {Mario Kummer and David Sawall},
journal= {arXiv preprint arXiv:2402.01272},
year = {2026}
}