Published on:

7 February 2024

Primary Category:

Group Theory

Paper Authors:

Marco Barbieri,

Pablo Spiga

•

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

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.

Cliques in derangement graphs of innately transitive groups

Dixon's asymptotic for random generation of symmetric group

On divergent on average trajectories for higher rank diagonal actions

Key properties of probabilistic derangement polynomials

Groups preserving subset orientation

Seymour's conjecture for random graph orientations

No comments yet, be the first to start the conversation...

Sign up to comment on this paper