We find a lower bound on the proportion of derangements in a finite transitive group that depends on the minimal nontrivial subdegree. As a consequence, we prove that, if Γ is a G-vertex-transitive digraph of valency d≥1, then the proportion of derangements in G is greater than 1/2d.
Barbieri, M., Spiga, P. (2024). On derangements and suborbits in finite transitive groups. DISCRETE MATHEMATICS, 347(7 (July 2024)) [10.1016/j.disc.2024.114032].
On derangements and suborbits in finite transitive groups
Spiga P.
2024
Abstract
We find a lower bound on the proportion of derangements in a finite transitive group that depends on the minimal nontrivial subdegree. As a consequence, we prove that, if Γ is a G-vertex-transitive digraph of valency d≥1, then the proportion of derangements in G is greater than 1/2d.
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