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This is a Quantitative Study study.

October 19, 2025Open Access

Explicit sumset sizes in additive number theory

Key Points

The study computes the range of sumset sizes of finite integer sets, revealing complex patterns.
It identifies infinite families of finite sets and calculates their respective h-fold sumset sizes.
Understanding sumset sizes is crucial for resolving open problems in additive number theory.
The results may guide further investigations into the properties of integers and additive structures.

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 Rₙ (h, k) = \|hA|: A {Z and |A|=k\} for all integers h 3 and k 3. This paper constructs certain infinite families of finite sets of size k and computes their h-fold sumset sizes.

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Cite This Study

Melvyn B. Nathanson (Thu,) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc696d73 https://doi.org/https://doi.org/10.48550/arxiv.2505.05329

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