标题： 一种对Ellenberg-Gijswijt美丽证明的有动机的阐述，该证明表明在$F_3^n$中没有三项等差数列的最大子集是$O(c^n)$，其中$c=\root 3 \of {(5589+891\,\sqrt {33})}/8=2.75510461302363300022127...$ 显示英文标题

标题： 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最近通过证明$F_3^n$中没有3项等差数列的最大子集的大小指数上小于大小$3^n$，即$F_3^n$的大小（更一般地，对于$q^n$，当$F_q^n$时）而令组合学界感到震惊。 在这里，我们提供了一个有说服力的、自顶向下的他们的美丽证明的描述，旨在让更广泛的受众欣赏它。 显示英文摘要

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.