An Erdős-Ko-Rado theorem for finite \(2\)-transitive groups

Date
2016
Authors
Meagher, Karen
Spiga, Pablo
Tiep, Pham Huu
Journal Title
Journal ISSN
Volume Title
Publisher
European Journal of Combinatorics
Abstract

We prove an analogue of the classical Erdős-Ko-Rado theorem for intersecting sets of permutations in finite (2)-transitive groups. Given a finite group (G) acting faithfully and (2)-transitively on the set (\Omega), we show that an intersecting set of maximal size in (G) has cardinality (|G|/|\Omega|). This generalises and gives a unifying proof of some similar recent results in the literature.

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Keywords
derangement graph, independent sets, Erd\H{o}s-Ko-Rado theorem
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