2022/06/20 by Henry Robert Thackeray, Thackeray, Henry Robert
Computer Science · Engineering · Mathematics · #05B25 #05D99 #51E15 (Secondary) #51E20 (Primary) 05B40 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.2206.09804
openalex publication_date 2022/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An s-cap n-flat is given by a set of s points, no three of which are on a common line, in an n-dimensional affine space over the field of three elements. The cap set problem in dimension n is: what is the maximum s such that there is an s-cap n-flat? The first two papers in this series of articles considered the cap set problem in dimensions up to and including 5. In this paper, which is the third in the series, we consider dimensions 6 and 7: we prove that every 110-cap 6-flat is a 112-cap 6-flat minus two cap points, and that there are no 289-cap 7-flats.