Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2021; 58(2): 305-313

Online first article March 5, 2021      Printed March 31, 2021

https://doi.org/10.4134/BKMS.b200054

Copyright © The Korean Mathematical Society.

Some inverse results of sumsets

Min Tang, Yun Xing

Anhui Normal University; Anhui Normal University

Abstract

Let $h\geq 2$ and $A=\{a_0,a_1,\ldots,a_{k-1}\}$ be a finite set of integers. It is well-known that $\left|hA\right|=hk-h+1$ if and only if $A$ is a $k$-term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets $A$ with some extremal the cardinalities of $hA$.

Keywords: Sumsets, inverse problem, arithmetic progression

MSC numbers: 11B13

Supported by: This work was supported by the National Natural Science Foundation of China(Grant No. 11971033) and top talents project of Anhui Department of Education(Grant No. gxbjZD05)