This analysis computes sumset sizes in additive number theory, suggesting insights into finite integer sets.
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 RZ(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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Melvyn B. Nathanson (2025) studied this question.
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