论文信息 - On almost Cap sets in three variables and the multivariable Cap set problem

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

In this note we prove that almost cap sets A ⊂ Fq , i.e., the subsets of Fq that do not contain too many arithmetic progressions of length three, satisfy that |A| < cq for some cq < q. As a corollary we prove a multivariable analogue of Ellenberg-Gijswijt theorem [3].

Alexander Fish | Dibyendu Roy

[1] Jordan S. Ellenberg,et al. On large subsets of $F_q^n$ with no three-term arithmetic progression , 2016 .

[2] Ernie Croot,et al. Progression-free sets in Z_4^n are exponentially small , 2016, 1605.01506.

[3] Shachar Lovett. The analytic rank of tensors and its applications , 2018, 1806.09179.