sumset

和集

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

For subsets A,B of an additively written abelian group, their sumset A+B is {a+b:a∈A,b∈B}; each resulting element is included once, regardless of representation multiplicity.

加法记号的阿贝尔群中，子集 A、B 的和集 A+B 是所有 a+b 构成的集合；同一个和值无论有多少种表示，都只计一个元素。

Example

$\{0,2\}+\{0,3\}=\{0,2,3,5\}$.

Usage and distinctions

A+A allows equal summands and is not the dilation {2a:a∈A}; restricted sumsets impose extra conditions not present here.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Ben Green — Additive Combinatorics, Oxford C3.10 (2024–25)Section 0.1 Overview, sumset A+A definition; Section 3.5, pair-of-sets sumset convention · Checked 2026-10-14

Translation sources

1. 数学年刊A辑（复旦大学）— 整数中限制符号和集的一些逆问题文章记录，中文关键词「和集」与英文关键词「Sumset」；名称证据，不作为普通和集定义来源 · Checked 2026-10-14

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