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arXiv · 2505.05329

Explicit sumset sizes in additive number theory

Melvyn B. Nathanson
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Abstract

It is an open problem in additive number theory to compute and understand the full range of sumset sizes of finite sets of integers, that is, the set $\mathcal{R}_{\mathbf{Z}}(h,k)= \{|hA|:A \subseteq {\mathbf{Z}} \text{ and } |A|=k\}$ for all integers $h \geq 3$ and $k \geq 3$. This paper constructs certain infinite families of finite sets of size $k$ and computes their $h$-fold sumset sizes.

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Melvyn B. Nathanson. 2025-05-08. Explicit sumset sizes in additive number theory. https://doi.org/10.4153/s0008439525101549

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