
Recent Posts
 Affine Images of Infinite sets
 Additive transversality of fractal sets in the reals and the integers
 Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
 Distal systems and Expansive systems
 Structure of multicorrelation sequences with integer part polynomial iterates along primes
Tag Archives: erdos
Affine Images of Infinite sets
— 1. Szemerédi’s theorem as affine images — Szemerédi’s theorem is usually stated as “every set with positive upper density contains arbitrarily long arithmetic progressions”, but it can also be formulated without explicit mention of arithmetic progressions: Theorem 1 (Szemerédi’s … Continue reading
Posted in Analysis, Combinatorics, Ramsey Theory
Tagged Affine transformations, Bourgain, erdos, Szemeredi's theorem
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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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Weighted densities with multiplicative structure
The upper density of a set , defined by provides a useful way to measure subsets of . For instance, whenever , contains arbitrarily long arithmetic progressions, this is Szemerédi’s theorem. A fundamental property of the upper density is that … Continue reading
Posted in Combinatorics, Number Theory, Tool
Tagged erdos, multiplicative structure, Upper density, weighted densities
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