Separating subsets from their imagesBarbieri, Marco (Avtor) Lekše, Maruša (Avtor) Potočnik, Primož (Avtor) Rekvényi, Kamilla (Avtor) permutation groupstransitive groupsprimitive groupsself-separable setLet $G$ be a transitive permutation group acting on $\Omega$. In this paper, we introduce and study the parameter ${\mathrm {sep}}(G)$, which denotes the size of the smallest set of points $A$ such that, for every permutation $g\in G$, $A \cap A^g$ is nonempty. In particular, we focus on deriving general bounds for arbitrary transitive groups, and on the asymptotic behaviour of certain families of primitive groups. We also provide a classification of transitive groups with ${\mathrm {sep}}(G)$ largest possible, namely with ${\mathrm {sep}}(G)=\lceil (|\Omega |+1) / 2 \rceil$.20262026-07-23 12:45:07Neznano31267sl