Tag Archives: density

A proof of the Erdős sumset conjecture

Florian Richter, Donald Robertson and I have uploaded to the arXiv our paper entitled A proof of the Erdős sumset conjecture. The main goal of the paper is to prove the following theorem, which verifies a conjecture of Erdős discussed … Continue reading

Posted in Combinatorics, paper | Tagged , , , , , , , | Leave a comment

Erdős Sumset conjecture

Hindman’s finite sums theorem is one of the most famous and useful theorems in Ramsey theory. It states that for any finite partition of the natural numbers, one of the cells of this partition contains an IP-set, i.e., there exists … Continue reading

Posted in Combinatorics, Number Theory, State of the art | Tagged , , , , , , , | 4 Comments

Brauer’s theorem and a coloring trick of Bergelson

— 1. Introduction — Ramsey theory concerns essentially two types of results: coloring and density results. Coloring results state that given a finite partition of some structured set (usually ) one of the cells in the partition still has some … Continue reading

Posted in Combinatorics, Ergodic Theory, Ramsey Theory, Tool | Tagged , , , , , , | 3 Comments