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

Xuancheng Shao

doi:10.19086/da.9095

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

Xuancheng Shao

Mathematics

Producción científica: Article › revisión exhaustiva

7 Citas (Scopus)

Resumen

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|.

Idioma original	English
Número de artículo	12
Publicación	Discrete Analysis
Volumen	2019
DOI	https://doi.org/10.19086/da.9095
Estado	Published - 2019

Nota bibliográfica

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

Financiación

\u2217Supported by the NSF grant DMS-1802224.

Financiadores	Número del financiador
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	1802224

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.19086/da.9095

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AB - 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|.

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