The excluded minors for GF(5)-representable matroids on ten elements
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908321153286144 |
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| author | Brettell, Nick |
| author_facet | Brettell, Nick |
| contents | Mayhew and Royle (2008) showed that there are 564 excluded minors for the class of GF(5)-representable matroids having at most 9 elements. We enumerate the excluded minors for GF(5)-representable matroids having 10 elements: there are precisely 2128 such excluded minors. In the process we find, for each $i \in \{2,3,4\}$, the excluded minors for the class of $\mathbb{H}_i$-representable matroids having at most 10 elements, and the excluded minors for the class of $\mathbb{H}_5$-representable matroids having at most 13 elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The excluded minors for GF(5)-representable matroids on ten elements Brettell, Nick Combinatorics Mayhew and Royle (2008) showed that there are 564 excluded minors for the class of GF(5)-representable matroids having at most 9 elements. We enumerate the excluded minors for GF(5)-representable matroids having 10 elements: there are precisely 2128 such excluded minors. In the process we find, for each $i \in \{2,3,4\}$, the excluded minors for the class of $\mathbb{H}_i$-representable matroids having at most 10 elements, and the excluded minors for the class of $\mathbb{H}_5$-representable matroids having at most 13 elements. |
| title | The excluded minors for GF(5)-representable matroids on ten elements |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2307.14614 |