数学季刊 ›› 2025, Vol. 40 ›› Issue (4): 352-359.doi: 10.13371/j.cnki.chin.q.j.m.2025.04.002

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有限整数和集问题研究综述

  

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China
  • 收稿日期:2025-06-25 出版日期:2025-12-30 发布日期:2025-12-30
  • 作者简介:TANG Min (1977-), female, native of Liuan, Anhui, professor of Anhui Normal University, engages in combinatorial number theory.
  • 基金资助:
    Supported by National Natural Science Foundation of China (Grant No. 12371003).

A Survey on Sumset Problems of Finite Integer Sets

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China
  • Received:2025-06-25 Online:2025-12-30 Published:2025-12-30
  • About author:TANG Min (1977-), female, native of Liuan, Anhui, professor of Anhui Normal University, engages in combinatorial number theory.
  • 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

Abstract: 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.

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

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