On sumsets of nonbases of maximum size

Bela Bajnok; Peter Pal Pach

On sumsets of nonbases of maximum size

Number Theory 2022-11-28 v1

Authors: Bela Bajnok , Peter Pal Pach

Abstract

Let $G$ be a finite abelian group. A nonempty subset $A$ in $G$ is called a basis of order $h$ if $hA=G$ ; when $hA \neq G$ , it is called a nonbasis of order $h$ . Our interest is in all possible sizes of $hA$ when $A$ is a nonbasis of order $h$ in $G$ of maximum size; we provide the complete answer when $h=2$ or $h=3$ .

Keywords

finite abelian group basis of order h nonbasis sumset maximal size additive number theory

Cite

@article{arxiv.2211.13678,
  title  = {On sumsets of nonbases of maximum size},
  author = {Bela Bajnok and Peter Pal Pach},
  journal= {arXiv preprint arXiv:2211.13678},
  year   = {2022}
}

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