Improved bounds on sizes of generalized caps in $AG(n,q)$

Michael Tait; Robert Won

doi:10.1137/20M1369439

Improved bounds on sizes of generalized caps in $AG(n,q)$

Combinatorics 2022-10-04 v2 Number Theory

Authors: Michael Tait , Robert Won

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

An $m$ -general set in $AG(n,q)$ is a set of points such that any subset of size $m$ is in general position. A $3$ -general set is often called a capset. In this paper, we study the maximum size of an $m$ -general set in $AG(n,q)$ , significantly improving previous results. When $m=4$ and $q=2$ we give a precise estimate, solving a problem raised by Bennett.

Keywords

general set capset affine geometry maximum size bounds

Cite

@article{arxiv.2002.09521,
  title  = {Improved bounds on sizes of generalized caps in $AG(n,q)$},
  author = {Michael Tait and Robert Won},
  journal= {arXiv preprint arXiv:2002.09521},
  year   = {2022}
}

Comments

Revised version. To appear in SIAM Journal on Discrete Mathematics

Related papers

View all related →