M. Nathanson

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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.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…

math.NT2026

Sumset size races for measurable sets

Melvyn B. Nathanson

Let $G$ be a locally compact abelian group with Haar measure $I^¼$ . For integers $n \geq 2$ and $H \geq 2$ and for any $n$ -tuples $\mathbf{u}_1,\ldots, \mathbf{u}_H \in \mathbf{N}^n…

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

Arithmetical structure of sumset intersections

Sumset size races for measurable sets

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

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