20.500.12556/RUL-185118 Separating subsets from their images Let $G$ 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 ${\mathrm {sep}}(G)=\lceil (|\Omega |+1) / 2 \rceil$. permutation groups transitive groups primitive groups self-separable set true false true Angleški jezik Angleški jezik Članek v reviji 2026-07-23 12:45:40 2026-07-23 12:45:43 2026-07-24 04:07:22 0000-00-00 00:00:00 2026 0 0 47 str. art. e111 Vol. 14 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512:519.1 2050-5094 10.1017/fms.2026.10258 285574915 separating-subsets-from-their-images.pdf separating-subsets-from-their-images.pdf 1 51FFCAA8844095CFD667B2CF404AD004 613014f25ec2937d1a995f743e0ed7f6d7c3782e2ff454ed68b4694ed2601a4b ad3e1ea0-8683-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=243329 https://doi.org/10.1017/fms.2026.10258 1 6a3443d5-8683-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=243328 Fakulteta za matematiko in fiziko 0 0 0