M. Nathanson

collaborators

18 papers

math.NT2026

Sidon sets with $Δ$ -separated sumsets in additive number theory

Melvyn B. Nathanson

The nonempty set $A$ of integers is $Δ$ -separated if $∣ a - a^{'} ∣ \geq Δ$ for all $a, a^{'} \in A$ with $a \neq = a^{'}$ . The set $A$ is a $B_{h}$ -set if every element of the sumset $h A$ has a uni…

math.NT2026

A problem on sumset sizes of sets of lattice points

Melvyn B. Nathanson

A central problem in additive number theory is to understand the set of sizes of $h$ -fold sums of finite subsets of an additive abelian semigroup. It is proved that the "range of s…

math.NT2026

Problems in additive number theory, VII: The structure of additive $h$ -bases for $n$

Melvyn B. Nathanson

In additive number theory, a finite set $A$ of integers is an $h$ -basis for $n$ if every integer in ${0, 1, 2, \dots, n}$ can be represented as the sum of exactly $h$ not necessari…

math.NT2026

Diversity, equity, and inclusion for problems in additive number theory

Melvyn B. Nathanson

This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the a…

math.CO2026

Problems and results on intersections of product sets and sumsets in semigroups

Melvyn B. Nathanson

For every subset $A$ of a semigroup $S$ , let $A^{h}$ be the set of all products of $h$ elements of $S$ . If $(A)_{q \in Q}$ is a family of subsets of $S$ , then $A = \bigcap_{q \in Q} A…

math.NT2026

Arithmetical structure of sumset intersections

Diego Marques, Melvyn B. Nathanson

The $h$ -fold sumset of a set $A$ of integers is the set of all sums of $h$ not necessarily distinct elements of $A$ . Let $(A_{q})_{q = 1}^{\infty}$ be a strictly decreasing sequence of…

Sidon sets with Δ-separated sumsets in additive number theory

A problem on sumset sizes of sets of lattice points

Problems in additive number theory, VII: The structure of additive h-bases for n

Diversity, equity, and inclusion for problems in additive number theory

Problems and results on intersections of product sets and sumsets in semigroups

Arithmetical structure of sumset intersections

Sidon sets with $Δ$ -separated sumsets in additive number theory

Problems in additive number theory, VII: The structure of additive $h$ -bases for $n$