On simple matroids with a unique minimal tropical basis
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914842394230784 |
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| author | Hochstättler, Winfried |
| author_facet | Hochstättler, Winfried |
| contents | In this note we characterize tropical bases as sets of circuits that by orthogonality determine the set of cocircuits of a simple matroid. Furthermore, we show that any circuit, which itself is closed, must be contained in any tropical basis. This yields a characterization of simple matroids which have a unique minimal tropical basis, giving a solution for a problem posted in the Matroid Union Blog. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On simple matroids with a unique minimal tropical basis Hochstättler, Winfried Combinatorics 05B35 In this note we characterize tropical bases as sets of circuits that by orthogonality determine the set of cocircuits of a simple matroid. Furthermore, we show that any circuit, which itself is closed, must be contained in any tropical basis. This yields a characterization of simple matroids which have a unique minimal tropical basis, giving a solution for a problem posted in the Matroid Union Blog. |
| title | On simple matroids with a unique minimal tropical basis |
| topic | Combinatorics 05B35 |
| url | https://arxiv.org/abs/2406.14244 |