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Tag Archives: density
A proof a sumset conjecture of Erdős
Florian Richter, Donald Robertson and I have uploaded to the arXiv our paper entitled A proof a sumset conjecture of Erdős. 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 density, erdos, Richter, Robertson, StoneCech compactification, sumset, Ultrafilters, weak mixing
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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 IPset, i.e., there exists … Continue reading
Posted in Combinatorics, Number Theory, State of the art
Tagged Banach density, Bohr sets, density, erdos, Jin, sumset, Ultrafilters, weak mixing
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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 Bergelson, coloring, coloring trick, density, ramsey theory, Szemeredi's theorem, van der waerden
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