Separating subsets from their images
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917161907257344 |
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| author | Barbieri, Marco Lekše, Maruša Potočnik, Primož Rekvényi, Kamilla |
| author_facet | Barbieri, Marco Lekše, Maruša Potočnik, Primož Rekvényi, Kamilla |
| contents | Let $G$ be a transitive permutation group acting on $Ω$. In this paper, we introduce and study the parameter ${\bf m}(G)$, 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 ${\bf m}(G)$ largest possible, namely with ${\bf m}(G)=\lceil (|Ω|+1) / 2 \rceil$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separating subsets from their images Barbieri, Marco Lekše, Maruša Potočnik, Primož Rekvényi, Kamilla Group Theory Combinatorics 20B05, 05B30, 20B15, 20B25 Let $G$ be a transitive permutation group acting on $Ω$. In this paper, we introduce and study the parameter ${\bf m}(G)$, 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 ${\bf m}(G)$ largest possible, namely with ${\bf m}(G)=\lceil (|Ω|+1) / 2 \rceil$. |
| title | Separating subsets from their images |
| topic | Group Theory Combinatorics 20B05, 05B30, 20B15, 20B25 |
| url | https://arxiv.org/abs/2508.20731 |