M. Nathanson

activity

20002026

most citedUnique representation bases for the integers

34 citations · 268 across the 120 of their papers we have counts for

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Showing 2015 · math.NTShow all

4 papers · 2 filters

math.NT2015

Cantor polynomials and the Fueter-Polya theorem

Melvyn B. Nathanson

A packing polynomial is a polynomial that maps the set $N_{0}^{2}$ of lattice points with nonnegative coordinates bijectively onto $N_{0}$ . Cantor constructed two quadr…

math.NT2015

Sums of sets of lattice points and unimodular coverings of polytopes

Melvyn B. Nathanson

If $P$ is a lattice polytope (that is, the convex hull of a finite set of lattice points in $R^{n}$ ), then every sum of $h$ lattice points in $P$ is a lattice point in the $…

math.NT2015

Pick's theorem and sums of lattice points

Karl Levy, Melvyn B. Nathanson

Pick's theorem is used to prove that if $P$ is a lattice polygon (that is, the convex hull of a finite set of lattice points in the plane), then every lattice point in the $h$ -fold…

math.NT2015★ 2 cited

Every finite set of integers is an asymptotic approximate group

Melvyn B. Nathanson

A set $A$ is an $(r, ℓ)$ -approximate group in the additive abelian group $G$ if $A$ is a nonempty subset of $G$ and there exists a subset $X$ of $G$ such that $∣ X ∣ \leq ℓ$ and…