Ellenberg-Gijswijt Gorge证明不含三项等差数列的$F_3^n$的最大子集是$O(c^n)$，且有$c=\root 3 \of {(5589+891\,\sqrt {33})}/8=2.75510461302363300022127...$
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 $c=\root 3 \of {(5589+891\,\sqrt {33})}/8=2.75510461302363300022127...$
摘要：
受Croot-Lev-Pach突破的启发，Jordan Ellenberg和Dion Gijswijt最近证明了没有3项等差数列的$F_3^n$的子集的最大尺寸以指数方式小于$F_3^n$的尺寸$3^n$（更一般地说，是$F_q^n$的$q^n$）。在这里，我们给出了一个有动机的，自上而下的，他们美丽的证明，旨在使它被更广泛的观众欣赏。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
