English

The cap set problem: 41-cap 5-flats

Combinatorics 2022-06-22 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2206.09719,
  title  = {The cap set problem: 41-cap 5-flats},
  author = {Henry Robert Thackeray},
  journal= {arXiv preprint arXiv:2206.09719},
  year   = {2022}
}

Comments

19 pages, 18 figures

R2 v1 2026-06-24T11:57:10.126Z