Wouter van Doorn

collaborators

10 papers

math.NT2026

Gaps in Multiplicative Sidon Sets

Wouter van Doorn, Pietro Monticone, Quanyu Tang

For a positive integer $n$ , let $g (n)$ denote the infimum of all real numbers $L$ such that there exists a multiplicative Sidon set $A \subseteq {1, 2, \dots, n}$ that intersects ever…

math.NT2026

The cardinality of a set containing the pairwise sums of a fixed number of integers

Wouter van Doorn

Revisiting a $50$ -year-old estimate of Choi, Erdős and Szemerédi, we show that if $A \subseteq {1, 2, \dots, 2 n}$ satisfies $∣ A ∣ \geq n + 1.2 \cdot 1 0^{8}$ , then there exist five d…

math.CO2026

Global Product Intersection Sets in Semigroups

Wouter van Doorn, Pietro Monticone, Quanyu Tang

For a family $(A_{q})_{q \in Q}$ of subsets of a semigroup, the product intersection set records those exponents $h \in N$ for which the $h$ -fold product set of the intersect…

math.CO2026

Optimal bounds for an Erdős problem on matching integers to distinct multiples

Wouter van Doorn, Yanyang Li, Quanyu Tang

Let $f (m)$ be the largest integer such that for every set $A = {a_{1} < \dots < a_{m}}$ of $m$ positive integers and every open interval $I$ of length $2 a_{m}$ , there exist at least $…

math.NT2026

On the length of an interval that contains distinct multiples of the first $n$ positive integers

Wouter van Doorn

Confirming a conjecture by Erd\H os and Pomerance, we prove that there exist intervals of length $\frac{c n l o g n}{l o g l o g n}$ that do not contain distinct multiples of $1, 2, \ld…

math.NT2025

Growth rates of sequences governed by the squarefree properties of its translates

Wouter van Doorn, Terence Tao

We answer several questions of Erdős regarding sequences of natural numbers $A$ whose translates $n + A$ intersect with the squarefree numbers in various specified ways. For instance…

math.NT2025

Smooth sums with small spacings

Wouter van Doorn, Anneroos R. F. Everts

Solving a problem by Erdős, we prove that every positive integer $n$ can be written as a sum $n = b_{1} + b_{2} + \dots + b_{r}$ of distinct $3$ -smooth integers with $1 \le b_{1…

math.NT2025

Improved bounds for the Mayer-Erdős phenomenon on similarly ordered Farey fractions

Wouter van Doorn

Let $\frac{a _{1}}{b _{1}}, \frac{a _{2}}{b _{2}}, \dots$ be the Farey fractions of order $n$ . We then prove that the inequality $(a_{l} - a_{k}) (b_{l} - b_{k}) \geq 0$ holds for all $k$ and $l > k$ w…

math.NT2025

Partitions with prescribed sum of reciprocals: asymptotic bounds

Wouter van Doorn

In $1963$ Graham proved that every positive integer $n \geq 78$ can be written as a sum of distinct positive integers $a_{1}, a_{2}, \dots, a_{r}$ for which $\frac{1}{a_1} + \frac{1}{a_2…

math.NT2025

Partitions with prescribed sum of reciprocals: computational results

Wouter van Doorn

For a positive rational $α$ , call a set of distinct positive integers ${a_{1}, a_{2}, \dots, a_{r}}$ an $α$ -partition of $n$ , if the sum of the $a_{i}$ is equal to $n$ and the sum of th…

Gaps in Multiplicative Sidon Sets

The cardinality of a set containing the pairwise sums of a fixed number of integers

Global Product Intersection Sets in Semigroups

Optimal bounds for an Erdős problem on matching integers to distinct multiples

On the length of an interval that contains distinct multiples of the first n positive integers

Growth rates of sequences governed by the squarefree properties of its translates

Smooth sums with small spacings

Improved bounds for the Mayer-Erdős phenomenon on similarly ordered Farey fractions

Partitions with prescribed sum of reciprocals: asymptotic bounds

Partitions with prescribed sum of reciprocals: computational results

On the length of an interval that contains distinct multiples of the first $n$ positive integers