Computing excluded minors for classes of matroids representable over partial fields
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916368077553664 |
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| author | Brettell, Nick Pendavingh, Rudi |
| author_facet | Brettell, Nick Pendavingh, Rudi |
| contents | We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field. Using these techniques, we enumerate the excluded minors on at most 15 elements for both the class of dyadic matroids, and the class of 2-regular matroids. We conjecture that there are no other excluded minors for the class of 2-regular matroids; whereas, on the other hand, we show that there is a 16-element excluded minor for the class of dyadic matroids. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_13175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing excluded minors for classes of matroids representable over partial fields Brettell, Nick Pendavingh, Rudi Combinatorics We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field. Using these techniques, we enumerate the excluded minors on at most 15 elements for both the class of dyadic matroids, and the class of 2-regular matroids. We conjecture that there are no other excluded minors for the class of 2-regular matroids; whereas, on the other hand, we show that there is a 16-element excluded minor for the class of dyadic matroids. |
| title | Computing excluded minors for classes of matroids representable over partial fields |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2302.13175 |