vix.ing · top · new · best · stats · spec

A Motivated Rendition of the Ellenberg-Gijswijt Gorgeous proof that the Largest Subset of F3n with No Three-Term Arithmetic Progression is O(cn), with c=\root 3 \of (5589+891 √ 33)/8=2.75510461302363300022127...

2016/07/06 by Doron Zeilberger, Zeilberger, Doron
Mathematics · #Analytic Number Theory Research #Benford’s Law and Fraud Detection #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO

paper · pdf · doi:10.48550/arxiv.1607.01804

7 pages. Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and this arxiv

arxiv created 2016/07/06 · openalex publication_date 2016/07/06 · arxiv updated 2016/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the Croot-Lev-Pach breakthrough, Jordan Ellenberg and Dion Gijswijt have recently amazed the combinatorial world by proving that the largest size of a subset of F3n with no 3-term arithmetic progressions is exponentially less than the size, 3n of F3n (and, more generally, qn for Fqn). Here we give a motivated, top-down, rendition of their beautiful proof, that aims to make it appreciated by a wider audience.

Related