A result on the size of iterated sumsets in $\mathbb{Z}^d$

Ilija Vrećica

A result on the size of iterated sumsets in $\mathbb{Z}^d$

Number Theory 2022-11-10 v2 Combinatorics

Authors: Ilija Vrećica

Abstract

In this paper we give a different approach to determining the cardinality of $h$ -fold sumsets $hA$ when $A\subset \mathbb{Z}^d$ has $d+2$ elements. This enables us to provide more general result with a shorter and simpler proof. We also obtain an upper bound for the value of $|hA|$ when $A\subset \mathbb{Z}^d$ is a set of $d+3$ elements with simplicial hull.

Keywords

iterated sumsets cardinality Z^d simplicial hull additive combinatorics

Cite

@article{arxiv.2109.04377,
  title  = {A result on the size of iterated sumsets in $\mathbb{Z}^d$},
  author = {Ilija Vrećica},
  journal= {arXiv preprint arXiv:2109.04377},
  year   = {2022}
}

Comments

It was noticed that the proof of the main Theorem could be improved to give a more general result. Also some motivating examples are provided

A result on the size of iterated sumsets in $\mathbb{Z}^d$

Abstract

Keywords

Cite

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