Excluding a line from $\mathbb C$-representable matroids
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910822529236992 |
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| author | Geelen, Jim Nelson, Peter Walsh, Zach |
| author_facet | Geelen, Jim Nelson, Peter Walsh, Zach |
| contents | For each positive integer $t$ and each sufficiently large integer $r$, we show that the maximum number of elements of a simple, rank-$r$, $\mathbb C$-representable matroid with no $U_{2,t+3}$-minor is $t{r\choose 2}+r$. We derive this as a consequence of a much more general result concerning matroids on group-labeled graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_12000 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Excluding a line from $\mathbb C$-representable matroids Geelen, Jim Nelson, Peter Walsh, Zach Combinatorics 05B35 For each positive integer $t$ and each sufficiently large integer $r$, we show that the maximum number of elements of a simple, rank-$r$, $\mathbb C$-representable matroid with no $U_{2,t+3}$-minor is $t{r\choose 2}+r$. We derive this as a consequence of a much more general result concerning matroids on group-labeled graphs. |
| title | Excluding a line from $\mathbb C$-representable matroids |
| topic | Combinatorics 05B35 |
| url | https://arxiv.org/abs/2101.12000 |