Tag Archives: monochromatic configurations

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

Posted in Combinatorics, Ramsey Theory, Tool | Tagged , , , , , , , , , | Leave a comment

New polynomial and multidimensional extensions of classical partition results

Vitaly Bergelson, John Johnson and I recently uploaded to the arXiv a paper entitled “New polynomial and multidimensional extensions of classical partition results“. In this post I will give some motivating examples for the results in the paper. To keep … Continue reading

Posted in Combinatorics, paper, Ramsey Theory | Tagged , , , , , | 1 Comment

Hales-Jewett and a generalized van der Warden Theorems

The Hales-Jewett 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 Hales-Jewett’s theorem is that … Continue reading

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

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