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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.11717 |
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| _version_ | 1866909350448070656 |
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| author | Barkley, Grant Tung, Katherine |
| author_facet | Barkley, Grant Tung, Katherine |
| contents | We show that, given a rank 3 affine root system $Φ$ with Weyl group $W$, there is a unique oriented matroid structure on $Φ$ which is $W$-equivariant and restricts to the usual matroid structure on rank 2 subsystems. Such oriented matroids were called oriented matroid root systems in Dyer-Wang (2021), and are known to be non-unique in higher rank. We also show uniqueness for any finite root system or "clean" rank 3 root system (which conjecturally includes all rank 3 root systems). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Oriented matroid structures on rank 3 root systems Barkley, Grant Tung, Katherine Combinatorics We show that, given a rank 3 affine root system $Φ$ with Weyl group $W$, there is a unique oriented matroid structure on $Φ$ which is $W$-equivariant and restricts to the usual matroid structure on rank 2 subsystems. Such oriented matroids were called oriented matroid root systems in Dyer-Wang (2021), and are known to be non-unique in higher rank. We also show uniqueness for any finite root system or "clean" rank 3 root system (which conjecturally includes all rank 3 root systems). |
| title | Oriented matroid structures on rank 3 root systems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.11717 |