Roth-type theorems in additive combinatroics
Combinatorics
2025-12-11 v2 Number Theory
Abstract
In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953. There were a number of generalized or improved results afterwards, which we call Roth-type theorems. We will list them and try to give concise expositions to the ideas in some of the proofs without much prior knowledge.
Cite
@article{arxiv.2512.08455,
title = {Roth-type theorems in additive combinatroics},
author = {Weiwen Zhang},
journal= {arXiv preprint arXiv:2512.08455},
year = {2025}
}