An Erdos-Ko-Rado theorem for finite 2-transitive groups

Karen Meagher; Pablo Spiga; Pham Huu Tiep

doi:10.1016/j.ejc.2016.02.005

An Erdos-Ko-Rado theorem for finite 2-transitive groups

Karen Meagher, Pablo Spiga, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We prove an analogue of the classical Erdos-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 Ω, we show that an intersecting set of maximal size in G has cardinality |G|/|Ω|. This generalises and gives a unifying proof of some similar recent results in the literature.

Original language	English (US)
Pages (from-to)	100-118
Number of pages	19
Journal	European Journal of Combinatorics
Volume	55
DOIs	https://doi.org/10.1016/j.ejc.2016.02.005
State	Published - Jul 1 2016

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2016.02.005

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title = "An Erdos-Ko-Rado theorem for finite 2-transitive groups",

abstract = "We prove an analogue of the classical Erdos-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 Ω, we show that an intersecting set of maximal size in G has cardinality |G|/|Ω|. This generalises and gives a unifying proof of some similar recent results in the literature.",

author = "Karen Meagher and Pablo Spiga and Tiep, {Pham Huu}",

note = "Funding Information: The first author was supported by NSERC Discovery Research Grant, Application No.: RGPIN- 341214-2013 . The third author was partially supported by the National Science Foundation grant DMS-1201374 and the Simons Foundation Fellowship 305247 . Publisher Copyright: {\textcopyright} 2016 Elsevier Ltd.",

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AU - Tiep, Pham Huu

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N2 - We prove an analogue of the classical Erdos-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 Ω, we show that an intersecting set of maximal size in G has cardinality |G|/|Ω|. This generalises and gives a unifying proof of some similar recent results in the literature.

AB - We prove an analogue of the classical Erdos-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 Ω, we show that an intersecting set of maximal size in G has cardinality |G|/|Ω|. This generalises and gives a unifying proof of some similar recent results in the literature.

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An Erdos-Ko-Rado theorem for finite 2-transitive groups

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