English

On the density of Kravitz sets

Number Theory 2025-10-21 v1 Combinatorics

Abstract

We show that for a subset AA of the cyclic group of prime order p>3p>3, if the sumset A+A2AA+A-2A is not the whole group, then A27p|A|\le \frac27\,p. Besides combinatorial arguments, we utilize a general technique involving linear programming.

Keywords

Cite

@article{arxiv.2510.16522,
  title  = {On the density of Kravitz sets},
  author = {Vsevolod Lev and Máté Matolcsi and Péter Pál Pach and Dániel Varga},
  journal= {arXiv preprint arXiv:2510.16522},
  year   = {2025}
}
R2 v1 2026-07-01T06:45:04.162Z