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Proportion of permutations without fixed points

Published on:

7 February 2024

Primary Category:

Group Theory

Paper Authors:

Marco Barbieri,

Pablo Spiga


Key Details

New lower bound on derangement percentage using minimal subdegree

Bound is at least 1/2d for vertex-transitive graph automorphisms

Compare bound with previous Cameron-Cohen bound

Examples where new bound is better

Open question on asymptotic superiority

AI generated summary

Proportion of permutations without fixed points

This paper proves a lower bound on the percentage of derangements (permutations without fixed points) in a finite transitive group, based on the minimal nontrivial subdegree. As an application, they show the derangement percentage in a vertex-transitive graph's automorphism group is at least 1/2d, where d is the graph valency.

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