
Recent Posts
 An arithmetic van der Corput trick and the polynomial van der Waerden theorem
 Piecewise syndetic sets, topological dynamics and ultrafilters
 Measure preserving actions of affine semigroups and {x+y,xy} patterns
 Szemerédi Theorem Part VI – Dichotomy between weak mixing and compact extension
 Gaussian systems
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
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 Bergelson, Deuber, Johnson, monochromatic configurations, polynomials, Rado
1 Comment
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
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