On an Almost All Version of the Balog-Szemerédi-Gowers Theorem

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Abstract

We deduce, as a consequence of the arithmetic removal lemma, an almost-all version of the Balog-Szemerédi-Gowers theorem. It states that for any K ≥ 1 and ε > 0, there exists δ = δ(K,ε) > 0 such that the following statement holds: if |A+ΓA| ≤ K|A| for some Γ ≥ (1-δ)|A|2, then there is a subset A' ⊂ A with |A'| ≥ (1-ε)|A| such that |A'+A'| ≤ |A+ΓA|+ε|A|.

Original languageEnglish
Article number12
JournalDiscrete Analysis
Volume2019
DOIs
StatePublished - 2019

Bibliographical note

Funding Information:
∗Supported by the NSF grant DMS-1802224.

Publisher Copyright:
© Licensed under a Creative Commons Attribution License (CC-BY)

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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