Extended inverse theorems for $h$-fold sumsets in integers

Mohan; Ram Krishna Pandey

Extended inverse theorems for $h$-fold sumsets in integers

Number Theory 2024-01-10 v1

Authors: Mohan , Ram Krishna Pandey

Abstract

Let $h \geq 2$ , $k \geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \left|hA\right| \leq hk+2h-3$ . In this paper, we extend the work of Tang and Xing and study all possible inverse theorems for $hk-h+1<\left|hA\right| \leq hk+3h-4$ . Furthermore, we give a range of $|hA|$ for which inverse problems are not possible.

Keywords

inverse theorems h-fold sumsets integers additive combinatorics sumset size finite sets

Cite

@article{arxiv.2401.04699,
  title  = {Extended inverse theorems for $h$-fold sumsets in integers},
  author = {Mohan and Ram Krishna Pandey},
  journal= {arXiv preprint arXiv:2401.04699},
  year   = {2024}
}

Comments

To be appear in contrib. discrete math., 17 pages, correct some typographical errors, Statement and proof of some results changed

Extended inverse theorems for $h$-fold sumsets in integers

Abstract

Keywords

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