Counting plane arrangements via oriented matroids
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908320850247680 |
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| author | Forcey, Stefan |
| author_facet | Forcey, Stefan |
| contents | Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets: the planes can intersect or not. Here we review how oriented matroids can be used to try to capture the combinatorial aspect, giving a way to encode with finite sets all the ways that $n$ planes can interact. We mention how the one-to-one correspondence breaks down in 2 dimensions for 9 lines, and in 3D for 8 planes. We include illustrations of all the types of plane arrangements using $n=4$ and 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting plane arrangements via oriented matroids Forcey, Stefan History and Overview Combinatorics 05B35, 52B40, 52C40 Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets: the planes can intersect or not. Here we review how oriented matroids can be used to try to capture the combinatorial aspect, giving a way to encode with finite sets all the ways that $n$ planes can interact. We mention how the one-to-one correspondence breaks down in 2 dimensions for 9 lines, and in 3D for 8 planes. We include illustrations of all the types of plane arrangements using $n=4$ and 5. |
| title | Counting plane arrangements via oriented matroids |
| topic | History and Overview Combinatorics 05B35, 52B40, 52C40 |
| url | https://arxiv.org/abs/2504.11461 |