有限整数和集问题研究综述

汤敏

doi:10.13371/j.cnki.chin.q.j.m.2025.04.002

数学季刊 >

2025 , Vol. 40 >Issue 4: 352 - 359

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.04.002

有限整数和集问题研究综述

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School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China

TANG Min (1977-), female, native of Liuan, Anhui, professor of Anhui Normal University, engages in combinatorial number theory.

收稿日期: 2025-06-25

网络出版日期: 2025-12-30

基金资助

Supported by National Natural Science Foundation of China (Grant No. 12371003).

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A Survey on Sumset Problems of Finite Integer Sets

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School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China

TANG Min (1977-), female, native of Liuan, Anhui, professor of Anhui Normal University, engages in combinatorial number theory.

Received date: 2025-06-25

Online published: 2025-12-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 12371003).

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摘要

Let A be a finite set of integers. For any integer h≥2, let hA and h ^∧A be the sets of all sums of h elements of A and all sums of h distinct elements of A, respectively. In this paper, we survey some significant advances in additive combinatorics concerning the size and structure of sumsets of finite integer sets.

关键词： Sumset; Restricted sumset; Small doubling; Freiman-Lev conjecture

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汤敏 . 有限整数和集问题研究综述[J]. 数学季刊, 2025 , 40(4) : 352 -359 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.002

Abstract

Key words： Sumset; Restricted sumset; Small doubling; Freiman-Lev conjecture

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