Some remarks on sumsets and restricted sumsets
Bull. Korean Math. Soc.
Published online 2019 Mar 13
Min Tang and wenhui Wang
School of Mathematics and Statistics, Anhui Normal University
Abstract : Let $A$ be a finite set of integers. For any integer $h\geq 2$, let $h$-hold sumset $hA$ be the set of all sums of $h$ elements of $A$ and let $h$-hold 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
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