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Tag Archives: coloring
An arithmetic van der Corput trick and the polynomial van der Waerden theorem
The van der Corput difference theorem (or trick) was develop (unsurprisingly) by van der Corput, and deals with uniform distribution of sequences in the torus. Theorem 1 (van der Corput trick) Let be a sequence in a torus . If … Continue reading
Measure preserving actions of affine semigroups and {x+y,xy} patterns
Vitaly Bergelson and I have recently submitted to the arXiv our paper entitled `Measure preserving actions of affine semigroups and patterns’. The main purpose of this paper is to extend the results of our previous paper, establishing some partial progress … Continue reading
A proof of Deuber’s theorem using HalesJewett’s theorem
In my previous post I explained how Rado’s theorem follows from Deuber’s theorem (which in turn gives a little more than Rado’s theorem, in one direction). The main purpose of this post is to give a full proof of Deuber’s … Continue reading
HalesJewett and a generalized van der Warden Theorems
The HalesJewett theorem is one of the most fundamental results in Ramsey theory, implying the celebrated van der Waerden theorem on arithmetic progressions, as well an its multidimensional and IP versions. One interesting property of the HalesJewett’s theorem is that … Continue reading
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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