Speaker
Maruša Lekše
(Institute of Mathematics, Physics and Mechanics, Ljubljana)
Description
Let $G$ be a transitive permutation group of degree $n$. Let $\textbf{m}(G)$ be the largest integer such that, for every set $A$ of this size, we are guaranteed the existence of a permutation $g \in G$ such that $A\cap A^g$ is empty. By Neumann's Separation Lemma, we know that $\textbf{m}(G) \geq \sqrt{n}$. Experimental evidence suggests that, unless $G$ contains a large alternating subgroup, $\textbf{m}(G)$ grows asymptotically as $\mathcal{O}(\sqrt{n})$. We discuss for which families of permutation groups we can currently establish this expected bound.
This is joint work with Marco Barbieri, Kamilla Rekvényi and Primož Potočnik.
Authors
Kamilla Rekvényi
Marco Barbieri
Maruša Lekše
(Institute of Mathematics, Physics and Mechanics, Ljubljana)
Primož Potočnik
