How Many Cards Should You Lay Out in Quad-128: A Classification of Caps in AG(7,2)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929682236047360 |
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| author | Calta, Karianne Goldberg, Timothy E. Rose, Lauren L. |
| author_facet | Calta, Karianne Goldberg, Timothy E. Rose, Lauren L. |
| contents | We define a cap in the affine geometry AG(n,2) to be a subset in which every collection of four points is in general position. In this paper, we classify, up to affine equivalence, all caps in AG(7,2) of size k greater than or equal to 10. In particular, we show that there are two equivalence classes of 10-caps and one equivalence class of 11-caps, none of which are complete, and one equivalence class of 12-caps, which are both complete and of maximum size. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_11173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How Many Cards Should You Lay Out in Quad-128: A Classification of Caps in AG(7,2) Calta, Karianne Goldberg, Timothy E. Rose, Lauren L. Combinatorics 05B25, 51E10, 51E15 We define a cap in the affine geometry AG(n,2) to be a subset in which every collection of four points is in general position. In this paper, we classify, up to affine equivalence, all caps in AG(7,2) of size k greater than or equal to 10. In particular, we show that there are two equivalence classes of 10-caps and one equivalence class of 11-caps, none of which are complete, and one equivalence class of 12-caps, which are both complete and of maximum size. |
| title | How Many Cards Should You Lay Out in Quad-128: A Classification of Caps in AG(7,2) |
| topic | Combinatorics 05B25, 51E10, 51E15 |
| url | https://arxiv.org/abs/2501.11173 |