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 language | English |
|---|---|
| Article number | 12 |
| Journal | Discrete Analysis |
| Volume | 2019 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© Licensed under a Creative Commons Attribution License (CC-BY)
Funding
\u2217Supported by the NSF grant DMS-1802224.
| Funders | Funder number |
|---|---|
| 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