34 citations · 268 across the 120 of their papers we have counts for
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Representation functions of additive bases for abelian semigroups
Melvyn B. Nathanson
Let X = S \oplus G, where S is a countable abelian semigroup and G is a countably infinite abelian group such that {2g : g in G} is infinite. Let pi: X \to G be the projection map…
Polynomial growth of sumsets in abelian semigroups
Melvyn B. Nathanson, Imre Z. Ruzsa
Let S be an abelian semigroup, and A a finite subset of S. The sumset hA consists of all sums of h elements of A, with repetitions allowed. Let |hA| denote the cardinality of hA. E…
Additive number theory and the ring of quantum integers
Melvyn B. Nathanson
Let and be positive integers. For the quantum integer there is a natural polynomial addition such that and…
Unique representation bases for the integers
Melvyn B. Nathanson
Arbitrarily sparse sets A of integers are constructed with the property that every integer can be represented uniquely in the form n = a + a', where a and a' belong to the set A an…