Higher cosystoles of matroids
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910239090016256 |
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| author | Douthitt, James Dylan Israel, Elana Kennard, Lee |
| author_facet | Douthitt, James Dylan Israel, Elana Kennard, Lee |
| contents | We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class of regular matroids of rank at most six. To accomplish this, we show that it is increasing under matroid extensions and then estimate it for each of the maximal simple regular matroids of rank at most six. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20409 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher cosystoles of matroids Douthitt, James Dylan Israel, Elana Kennard, Lee Combinatorics 05B35, 05C35, 53C20 We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class of regular matroids of rank at most six. To accomplish this, we show that it is increasing under matroid extensions and then estimate it for each of the maximal simple regular matroids of rank at most six. |
| title | Higher cosystoles of matroids |
| topic | Combinatorics 05B35, 05C35, 53C20 |
| url | https://arxiv.org/abs/2605.20409 |