Adrian Beker

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math.CO2026

The inverse problem for the Steiner-Wiener index of trees

Adrian Beker, Rudi MrazoviÄ

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 MiliÄeviÄ, Rudi MrazoviÄ

Let $I^\pm (n)$ 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 l…

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 $I^c ◯ (n^{5/4})$ obtained by Pohoata and Zakharov…