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arXiv · 2402.05089

On the proportion of derangements and on suborbits in finite transitive groups

Marco Barbieri·Pablo Spiga
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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 $\Gamma$ is a $G$-vertex-transitive digraph of valency $d\ge 1$, then the proportion of derangements in $G$ is greater than $1/2d$.

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Marco Barbieri, Pablo Spiga. 2024-02-07. On the proportion of derangements and on suborbits in finite transitive groups. https://doi.org/10.1016/j.disc.2024.114032

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