A Note on Sumsets and Restricted Sumsets

Jagannath Bhanja

A Note on Sumsets and Restricted Sumsets

Combinatorics 2021-06-09 v1 Number Theory

Authors: Jagannath Bhanja

Abstract

In this note we find the optimal lower bound for the size of the sumsets $HA$ and $H\,\hat{}A$ over finite sets $H, A$ of nonnegative integers, where $HA = \bigcup_{h\in H} hA$ and $H\,\hat{}A = \bigcup_{h\in H} h\,\hat{}A$ . We also find the underlying algebraic structure of the sets $A$ and $H$ for which the size of the sumsets $HA$ and $H\,\hat{}A$ is minimum.

Keywords

combinatorial group theory additive combinatorics upper bounds

Cite

@article{arxiv.2106.04091,
  title  = {A Note on Sumsets and Restricted Sumsets},
  author = {Jagannath Bhanja},
  journal= {arXiv preprint arXiv:2106.04091},
  year   = {2021}
}

Comments

8 pages

Related papers

View all related →