Adrian Beker

activity

20202026

collaborators

7 papers

math.CO2026

The inverse problem for the Steiner-Wiener index of trees

Adrian Beker, Rudi Mrazović

For a connected graph $G$ and a set $S \subset V (G)$ , the Steiner distance $d_{G} (S)$ is the minimum number of edges in a connected subgraph of $G$ containing $S$ . The Steiner-Wiener…

math.CO2026

A note on the shortest law for the symmetric group

Adrian Beker, Luka Milićević, Rudi Mrazović

Let $α (n)$ denote the length of the shortest non-trivial two-variable law for the symmetric group $S_{n}$ . Buskin's quantitative subgroup-separability argument gives the classical lo…

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.CO2024

Improved bounds for skew corner-free sets

Adrian Beker

We construct skew corner-free subsets of $[n]^{2}$ of size $n^{2} exp (- O (lo g n))$ , thereby improving on recent bounds of the form $Ω (n^{5/4})$ obtained by Pohoata and Zakharov.…

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…

math.CO2020

The star avoidance game

Adrian Beker

Let $n, k$ be positive integers. The $(k + 1)$ -star avoidance game on $K_{n}$ is played as follows. Two players take it in turn to claim a (previously unclaimed) edge of the complete g…

The inverse problem for the Steiner-Wiener index of trees

A note on the shortest law for the symmetric group

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

Improved bounds for skew corner-free sets

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 star avoidance game

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