On almost Cap sets in three variables and the multivariable Cap set problem

Alexander Fish; Dibyendu Roy

On almost Cap sets in three variables and the multivariable Cap set problem

Number Theory 2021-02-24 v1 Combinatorics

Authors: Alexander Fish , Dibyendu Roy

Abstract

In this note we prove that almost cap sets $A \subset \mathbb{F}_q^n$ , i.e., the subsets of $\mathbb{F}_q^n$ that do not contain too many arithmetic progressions of length three, satisfy that $|A| < c_q^n$ for some $c_q < q$ . As a corollary we prove a multivariable analogue of Ellenberg-Gijswijt theorem.

Cite

@article{arxiv.2102.11496,
  title  = {On almost Cap sets in three variables and the multivariable Cap set problem},
  author = {Alexander Fish and Dibyendu Roy},
  journal= {arXiv preprint arXiv:2102.11496},
  year   = {2021}
}

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5 pages

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