20.500.12556/DiRROS-31267 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 Ni določen Neznano 2026-07-23 12:45:07 2026-07-23 12:45:07 2026-07-24 03:52:03 0000-00-00 00:00:00 2026 0 0 47 str. article no. e111 Vol. 14 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 512:519.1 2050-5094 10.1017/fms.2026.10258 285574915 separating-subsets-from-their-images.pdf separating-subsets-from-their-images.pdf 1 57BBA667919D6B70B26432C8F83BDB5C c9a40d6e607e8e5ca16943e02cf3db8758b05c666d3078de35e56a81f199cbc5 149f7b65-8684-11f1-812a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48287 https://doi.org/10.1017/fms.2026.10258 1 93fac1c5-8683-11f1-812a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48286 Inštitut za matematiko, fiziko in mehaniko 0 0 0