Some inverse results of sumsets

Min Tang; Yun Xing

Some inverse results of sumsets

Number Theory 2019-11-05 v1

Authors: Min Tang , Yun Xing

Abstract

Let $h\geq 2$ and $A=\{a_0,a_1,\ldots,a_{k-1}\}$ be a finite set of integers. It is well-known that $\left|hA\right|=hk-h+1$ if and only if $A$ is a $k$ -term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets $A$ with some extrema the cardinalities of $hA$ .

Keywords

sumsets inverse problems arithmetic progression finite sets of integers cardinality

Cite

@article{arxiv.1911.00854,
  title  = {Some inverse results of sumsets},
  author = {Min Tang and Yun Xing},
  journal= {arXiv preprint arXiv:1911.00854},
  year   = {2019}
}

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