| Title: | Separating subsets from their images |
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| Authors: | ID Barbieri, Marco (Author)
ID Lekše, Maruša (Author)
ID Potočnik, Primož (Author)
ID Rekvényi, Kamilla (Author) |
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| Files: |  PDF - Presentation file, download (681,64 KB)
MD5: 57BBA667919D6B70B26432C8F83BDB5C
 URL - Source URL, visit https://doi.org/10.1017/fms.2026.10258
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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 ${\mathrm {sep}}(G)=\lceil (|\Omega |+1) / 2 \rceil$. |
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| Keywords: | permutation groups, transitive groups, primitive groups, self-separable set |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 47 str. |
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| Numbering: | Vol. 14, article no. e111 |
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| PID: | 20.500.12556/DiRROS-31267  |
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| UDC: | 512:519.1 |
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| ISSN on article: | 2050-5094 |
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| DOI: | 10.1017/fms.2026.10258 |
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| COBISS.SI-ID: | 285574915 |
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| Note: |
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| Publication date in DiRROS: | 23.07.2026 |
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| Views: | 203 |
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| Downloads: | 158 |
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