On a method of Alweiss

TL;DR

This paper explains Alweiss's recent proof of Hindman's conjecture over the rationals and extends his method to demonstrate partition regularity of sums of distinct products over the rationals.

Contribution

It provides an exposition of Alweiss's proof and introduces a modification to prove partition regularity of sums of distinct products over the rationals.

Findings

Alweiss proved Hindman's conjecture over the rationals.

The method can be modified to show partition regularity of sums of distinct products.

The paper offers an accessible exposition of the proof.

Abstract

Recently, Alweiss settled Hindman's conjecture over the rationals. In this paper, we provide our own exposition of Alweiss' result, and show how to modify his method to also show that sums of distinct products are partition regular over the rationals.