2022/06/20 by Henry Robert Thackeray, Thackeray, Henry Robert
Computer Science · Engineering · #05B25 #05D99 #51E15 (Secondary) #51E20 (Primary) 05B40 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.2206.09719
openalex publication_date 2022/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An s-cap n-flat, or an n-dimensional cap of size s, is a pair (S,F) where F is an n-dimensional affine space over Z/3Z and the size-s subset S of F contains no triple of collinear points. The cap set problem in dimension n asks for the largest s for which an s-cap n-flat exists. This series of articles investigates the cap set problem in dimensions up to and including 7. This is the second paper in the series. By applying and adapting methods from the first paper in the series, we systematically classify all 5-dimensional caps of size at least 41.