论文标题
关于Alweiss的技术和形式的单色配置的一些评论
Some remarks on Alweiss's technique and monochromatic configuration of the form $\left\{ x,y,x+y,x\cdot y\right\} $ over Rationals
论文作者
论文摘要
在本文中，我们将探索一种使用Ultrafilter技术的Alweiss \ cite {key-1}的方法，以研究形式的单色分区的常规结构$ \ left \ left \ weft \ {x，y，y，x+y，x+y，x \ cdot y \ cdot y \ right \ rioncation $ vositions vocions vociless vob yvorriations vob bowen of bowen of bowen of bowen和sabok in \ ciete} key {key {key {key {key {key。我们的方法探讨了组合富含组合的每个成员都包含这些类型的配置。除此之外，我们还将证明，对于任何$ n \ in \ mathbb {n}，$这些集将包含$ \ left \ left \ weft \ {x，y，x+y，x+y，x \ cdot y^{n} \ right \} $的配置。
In this article, we will explore a recent method of Alweiss \cite{key-1} using ultrafilter technique to study monochromatic partition regular structure of the form $\left\{ x,y,x+y,x\cdot y\right\} $ over rationals, which is recently proved by Bowen, and Sabok in \cite{key-17}. Our methods explore that each member of combinatorially rich ultrafilters contains these types of configurations. Besides this, we will also prove that for any $n\in\mathbb{N},$ these sets will contain configuration of the form $\left\{ x,y,x+y,x\cdot y^{n}\right\}$, partially proved by Xiao in \cite{key-25}.
