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arXiv · 1607.01804

A Motivated Rendition of the Ellenberg-Gijswijt Gorgeous proof that the Largest Subset of $F_3^n$ with No Three-Term Arithmetic Progression is $O(c^n)$, with $c=\root 3 \of {(5589+891\,\sqrt {33})}/8=2.75510461302363300022127...$

Doron Zeilberger
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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 $F_3^n$ with no 3-term arithmetic progressions is exponentially less than the size, $3^n$ of $F_3^n$ (and, more generally, $q^n$ for $F_q^n$). Here we give a motivated, top-down, rendition of their beautiful proof, that aims to make it appreciated by a wider audience.

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Doron Zeilberger. 2016-07-06. A Motivated Rendition of the Ellenberg-Gijswijt Gorgeous proof that the Largest Subset of $F_3^n$ with No Three-Term Arithmetic Progression is $O(c^n)$, with $c=\root 3 \of {(5589+891\,\sqrt {33})}/8=2.75510461302363300022127...$. https://arxiv.org/abs/1607.01804

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