Bulletin of the
Korean Mathematical Society
BKMS

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

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2019; 56(3): 667-673

Online first article March 13, 2019      Printed May 31, 2019

https://doi.org/10.4134/BKMS.b180477

Copyright © The Korean Mathematical Society.

Some remarks on sumsets and restricted sumsets

Min Tang, Wenhui Wang

Anhui Normal University; Anhui Normal University

Abstract

Let $A$ be a finite set of integers. For any integer $h\geq 1$, let $h$-fold sumset $hA$ be the set of all sums of $h$ elements of $A$ and let $h$-fold restricted sumset $h^{\wedge}A$ be the set of all sums of $h$ distinct elements of $A$. In this paper, we give a survey of problems and results on sumsets and restricted sumsets of a finite integer set. In details, we give the best lower bound for the cardinality of restricted sumsets $2^{\wedge}A$ and $3^{\wedge}A$ and also discuss the cardinality of restricted sumset $h^{\wedge}A$.

Keywords: restricted sumset, pigeonhole principle

MSC numbers: 11B13

Supported by: This work was supported by National Natural Science Foundation of China, Grant No. 11471017

Stats or Metrics

Share this article on :

Related articles in BKMS