Explicit sumset sizes in additive number theory

2025/05/08 by Melvyn B. Nathanson, Nathanson, Melvyn B.
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Topology and Set Theory #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2505.05329

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 R_Z(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.

Related

• Compression and complexity for sumset sizes in additive number theory
• A problem on sumset sizes of sets of lattice points
• Triangular and tetrahedral number differences of sumset sizes in additive number theory
• Problems in additive number theory, VI: Sizes of sumsets
• Additive sumset sizes with tetrahedral differences