Note on the Theorem of Balog, Szemerédi, and Gowers

IF 1 2区数学 Q1 MATHEMATICS Combinatorica Pub Date : 2024-04-23 DOI:10.1007/s00493-024-00092-5

Christian Reiher, Tomasz Schoen

引用次数: 0

Abstract

We prove that every additive set A with energy \(E(A)\ge |A|^3/K\) has a subset \(A'\subseteq A\) of size \(|A'|\ge (1-\varepsilon )K^{-1/2}|A|\) such that \(|A'-A'|\le O_\varepsilon (K^{4}|A'|)\). This is, essentially, the largest structured set one can get in the Balog–Szemerédi–Gowers theorem.

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关于巴洛格、塞梅雷迪和高尔斯定理的说明

我们证明，每个具有能量 \(E(A)\ge |A|^3/K\) 的可加集 A 都有一个大小为 \(|A'|ge (1-\varepsilon )K^{-1/2}|A|\) 的子集 \(A'\subseteq A\) ，使得 \(|A'-A'|\le O_\varepsilon (K^{4}|A'|)\).从本质上讲，这是巴洛格-塞梅雷迪-高尔定理中可以得到的最大结构集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.

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