Analysis & PDE· 2012Q1
On the Bogolyubov–Ruzsa lemma
- 159citations
- Q1SCImago
- 2012year
Short summary
A new bound shows that for any finite subset A of an abelian group, 2A 2A contains a structured set (a coset progression) of significant size, specifically at least exp(O(log(1/K)))|A|, where K relates to the size of A+A.
AI-generated from the title and abstract; the full text is not read.
Key points
- 2A 2A contains a coset progression M.
- The dimension of M is at least O(log(1/K)).
- The size of M is at least exp(O(log(1/K)))|A|.
- K is derived from the size of A+A.
AI-generated from the title and abstract; the full text is not read.
Abstract
Our main result is that if A is a finite subset of an abelian group with jACAj 6 KjAj, then 2A 2A contains an O.logO.1 / 2K/-dimensional coset progression M of size at least exp.O.logO.1 / 2K//jAj.
The authors' abstract, as published at the source. Analysis & PDE, 2012 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics