additive combinatorics

加法组合学

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Translation evidence: Literature usage

Meaning in context

Additive combinatorics studies arithmetic configurations, additive growth, and structural inverse questions for finite sets, especially in integers and abelian groups.

加法组合学研究有限集合中的算术配置、加法增长及其逆向结构问题，典型背景是整数或阿贝尔群。

Example

For A={0,2,4,6}A=\{0,2,4,6\}, ∣A+A∣=7|A+A|=7 and AA contains three-term arithmetic progressions.

Usage and distinctions

The ambient group matters: a finite subgroup has doubling ratio one, while a nontrivial finite subgroup of the integers does not exist.

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Definition sources

  1. Ben Green — Additive Combinatorics, Oxford C3.10 (2024–25)Section 0.1 Overview; Section 3.5, Definitions 3.10–3.11 and Proposition 3.12; Section 4.1, Theorem 4.1 · Checked 2026-10-14

Translation sources

  1. 华东师范大学 — 2019年运筹学与控制论在校博士全日制培养方案PDF p.7，课程MATH0011120079「加法组合学 / Additive Combinatorics」 · Checked 2026-10-14
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