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How Many Cards Should You Lay Out in Quad-128: A Classification of Caps in AG(7,2)
- Publication Year :
- 2025
-
Abstract
- 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.<br />Comment: 33 pages, 2 figures, 3 tables
- Subjects :
- Mathematics - Combinatorics
05B25, 51E10, 51E15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2501.11173
- Document Type :
- Working Paper