Adrian Beker

collaborators

3 papers

math.NT2025

The Erdős--Moser sum-free set problem via improved bounds for $k$ -configurations

Adrian Beker

A $k$ -configuration is a collection of $k$ distinct integers $x_{1}, \dots, x_{k}$ together with their pairwise arithmetic means $\frac{x _{i} + x _{j}}{2}$ for $1 \leq i < j \leq k$ . Building…

math.CO2023

On a problem of Erdős and Graham about consecutive sums in strictly increasing sequences

Adrian Beker

We show the existence of a constant $c > 0$ such that, for all positive integers $n$ , there exist integers $1 \leq a_{1} < \dots < a_{k} \leq n$ such that there are at least $c n^{2}$ di…

math.CO2023

A protrusive ordering of 5 points not witnessed by any finite multiset

Adrian Beker

Given a finite set of points $C \subseteq R^{d}$ , we say that an ordering of $C$ is protrusive if every point lies outside the convex hull of the points preceding it. We giv…

The Erdős--Moser sum-free set problem via improved bounds for k-configurations

On a problem of Erdős and Graham about consecutive sums in strictly increasing sequences

A protrusive ordering of 5 points not witnessed by any finite multiset

The Erdős--Moser sum-free set problem via improved bounds for $k$ -configurations