Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME REMARKS ON SUMSETS AND RESTRICTED SUMSETS

  • Tang, Min (School of Mathematics and Statistics Anhui Normal University) ;
  • Wang, Wenhui (School of Mathematics and Statistics Anhui Normal University)
  • Received : 2018.05.17
  • Accepted : 2019.01.08
  • Published : 2019.05.31
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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 $h^{\wedge}A$.

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References

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