Some remarks on sumsets and restricted sumsets
Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 667-673
Published online March 13, 2019
Printed May 31, 2019
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
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