A Survey on Sumset Problems of Finite Integer Sets

TANG Min

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

Chinese Quarterly Journal of Mathematics >

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

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

A Survey on Sumset Problems of Finite Integer Sets

Expand

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).

Fold

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

Cite this article

TANG Min . A Survey on Sumset Problems of Finite Integer Sets[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(4) : 352 -359 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.002

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article