Intersection density of transitive groups of certain degrees
Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 289-297.

Two elements g and h of a permutation group G acting on a set V are said to be intersecting if v g =v h for some vV. More generally, a subset of G is an intersecting set if every pair of elements of is intersecting. The intersection density ρ(G) of a transitive permutation group G is the maximum value of the quotient ||/|G v | where runs over all intersecting sets in G and G v is a stabilizer of vV. In this paper the intersection density of transitive groups of degree twice a prime is determined, and proved to be either 1 or 2. In addition, it is proved that the intersection density of transitive groups of prime power degree is 1.

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DOI: 10.5802/alco.209
Classification: 05C25,  20B25
Keywords: intersection density, derangement, derangement graph, transitive permutation group
Hujdurović, Ademir 1; Kutnar, Klavdija 1; Marušič, Dragan 2, 3; Miklavič, Štefko 2, 4

1 University of Primorska UP IAM & UP FAMNIT Glagoljaška 8, 6000 Koper Slovenia
2 IMFM Jadranska 19, 1000 Ljubljana Slovenia
3 University of Primorska, UP IAM & UP FAMNIT Glagoljaška 8, 6000 Koper Slovenia
4 University of Primorska, UP IAM & UP FAMNIT, Glagoljaška 8, 6000 Koper Slovenia
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Hujdurović, Ademir; Kutnar, Klavdija; Marušič, Dragan; Miklavič, Štefko. Intersection density of transitive groups of certain degrees. Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 289-297. doi : 10.5802/alco.209. https://alco.centre-mersenne.org/articles/10.5802/alco.209/

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