M. Nathanson

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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.CO2025

$B_{h}$ -sets of real and complex numbers

Melvyn B. Nathanson

Let $K = R$ or $C$ . An $n$ -element subset $A$ of $K$ is a $B_{h}$ -set if every element of $K$ has at most one representation as the sum of $h$ not necessarily disti…

math.CO2024

The Muirhead-Rado inequality, 2: Symmetric means and inequalities

Melvyn B. Nathanson

Preliminary results from Nathanson [5] are used to prove the Muirhead and Rado inequalities.

math.CO2024

The Muirhead-Rado inequality, 1 Vector majorization and the permutohedron

Melvyn B. Nathanson

Let $a$ and $b$ be vectors in $R^{n}$ with nonnegative coordinates. Permuting the coordinates, we can assume that $a_{1} \geq \dots \geq a_{n}$ and $b_1 \geq…

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

Bh​-sets of real and complex numbers

The Muirhead-Rado inequality, 2: Symmetric means and inequalities

The Muirhead-Rado inequality, 1 Vector majorization and the permutohedron

$B_{h}$ -sets of real and complex numbers