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.
Min Tang, Wenhui Wang
Anhui Normal University; Anhui Normal University
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
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