Monthly Archives: August 2013

Applications of the coloring trick

— 1. Introduction — In a previous post I used a coloring trick of Bergelson to deduce Brauer’s theorem from Szemeredi’s theorem. In this post I will provide two more applications of the coloring trick. To put it simply, the … Continue reading

Posted in Number Theory | 1 Comment

On {x+y,xy} patterns in large sets of countable fields

Vitaly Bergelson and I have recently uploaded to the arXiv our joint paper `On patterns in large sets of countable fields‘. We prove a result concerning certain monochromatic structures in countable fields and a corresponding density version. Schur’s Theorem, proved … Continue reading

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