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Three results related to the half-plane property of matroids
Kummer, Mario1; Sawall, David2
1 Technische Universität Dresden Germany
2 Universität Konstanz Konstanz Germany
Algebraic Combinatorics, Volume 8 (2025) no. 1, pp. 1-15.

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 Brändén and D’León 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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.399
Classification: 05B35, 12D10
Keywords: matroids, half-plane property, real zero polynomials, hyperbolic polynomials

Kummer, Mario 1; Sawall, David 2

1 Technische Universität Dresden Germany
2 Universität Konstanz Konstanz Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Kummer, Mario; Sawall, David. Three results related to the half-plane property of matroids. Algebraic Combinatorics, Volume 8 (2025) no. 1, pp. 1-15. doi : 10.5802/alco.399. https://alco.centre-mersenne.org/articles/10.5802/alco.399/

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