Girth in $GF(q)$-representable matroids
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915267760619520 |
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| author | Davies, James Hatzel, Meike Knauer, Kolja McCarty, Rose Ueckerdt, Torsten |
| author_facet | Davies, James Hatzel, Meike Knauer, Kolja McCarty, Rose Ueckerdt, Torsten |
| contents | We prove a conjecture of Geelen, Gerards, and Whittle that for any finite field $GF(q)$ and any integer $t$, every cosimple $GF(q)$-representable matroid with sufficiently large girth contains either $M(K_t)$ or $M(K_t)^*$ as a minor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Girth in $GF(q)$-representable matroids Davies, James Hatzel, Meike Knauer, Kolja McCarty, Rose Ueckerdt, Torsten Combinatorics We prove a conjecture of Geelen, Gerards, and Whittle that for any finite field $GF(q)$ and any integer $t$, every cosimple $GF(q)$-representable matroid with sufficiently large girth contains either $M(K_t)$ or $M(K_t)^*$ as a minor. |
| title | Girth in $GF(q)$-representable matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.21797 |