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