Cameron–Liebler sets in permutation groups

D’haeseleer, Jozefien; Meagher, Karen; Pantangi, Venkata Raghu Tej

doi:10.5802/alco.363

D’haeseleer, Jozefien ¹; Meagher, Karen ²; Pantangi, Venkata Raghu Tej ²

¹ Department of Mathematics: Analysis Logic and Discrete Mathematics Ghent University Belgium
² Department of Mathematics and Statistics University of Regina Regina Saskatchewan S4S 0A2 Canada

Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1157-1182.

Abstract

Consider a group $G$ acting on a set $Ω$ . A $(G, Ω)$ -Cameron–Liebler set is a subset of $G$ , whose indicator function is a linear combination of the indicator functions of the cosets of the point stabilizers. We investigate Cameron–Liebler sets in permutation groups, with a focus on constructions of Cameron–Liebler sets for $2$ -transitive groups.

Received: 2023-08-16
Revised: 2024-02-11
Accepted: 2024-02-12
Published online: 2024-09-03

DOI: 10.5802/alco.363

Classification: 05C35, 05C69, 20B05
Keywords: Cameron–Liebler sets, permutation groups

Author's affiliations:

D’haeseleer, Jozefien ¹; Meagher, Karen ²; Pantangi, Venkata Raghu Tej ²

¹ Department of Mathematics: Analysis Logic and Discrete Mathematics Ghent University Belgium
² Department of Mathematics and Statistics University of Regina Regina Saskatchewan S4S 0A2 Canada

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Cameron{\textendash}Liebler sets in permutation groups},
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D’haeseleer, Jozefien; Meagher, Karen; Pantangi, Venkata Raghu Tej. Cameron–Liebler sets in permutation groups. Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1157-1182. doi : 10.5802/alco.363. https://alco.centre-mersenne.org/articles/10.5802/alco.363/

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