34 citations · 268 across the 120 of their papers we have counts for
4 papers · 2 filters
Inverse problems for sumset sizes of finite sets of integers
Melvyn B. Nathanson
Let be a finite set of integers and let be its -fold sumset. This paper investigates the sequence of sumset sizes , the relations between these…
Problems in additive number theory, VI: Sizes of sumsets
Melvyn B. Nathanson
This paper describes problems concerning the range of cardinalities of sumsets and restricted sumsets of finite subsets of the integers and finite subsets of ordered abelian groups…
Addition theorems in partially ordered groups
Melvyn B. Nathanson
Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results…
Additive number theory and the Dyson transform
Melvyn B. Nathanson
In 1942 Mann solved a famous problem, the conjecture, about the lower bound of the Shnirel'man density of sums of sets of positive integers. In 1945, Dyson generalized Mann's…