Three results related to the half-plane property of matroids
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911404671369216 |
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| author | Kummer, Mario Sawall, David |
| author_facet | Kummer, Mario Sawall, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three results related to the half-plane property of matroids Kummer, Mario Sawall, David Combinatorics 05B35 (Primary), 12D10 (Secondary) 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. |
| title | Three results related to the half-plane property of matroids |
| topic | Combinatorics 05B35 (Primary), 12D10 (Secondary) |
| url | https://arxiv.org/abs/2402.01272 |