Permutations contained in transitive subgroups
Discrete analysis (2016)
Voir la notice de l'article provenant de la source Scholastica
arXiv
In the first paper in this series we estimated the probability that a random permutation $π\in\mathcal{S}_n$ has a fixed set of a given size. In this paper, we elaborate on the same method to estimate the probability that $π$ has $m$ disjoint fixed sets of prescribed sizes $k_1,\dots,k_m$, where $k_1+\cdots+k_m=n$. We deduce an estimate for the proportion of permutations contained in a transitive subgroup other than $\mathcal{S}_n$ or $\mathcal{A}_n$. This theorem consists of two parts: an estimate for the proportion of permutations contained in an imprimitive transitive subgroup, and an estimate for the proportion of permutations contained in a primitive subgroup other than $\mathcal{S}_n$ or $\mathcal{A}_n$.
Sean Eberhard; Kevin Ford; Dimitris Koukoulopoulos. Permutations contained in transitive subgroups. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a7/
@article{DAS_2016_a7,
author = {Sean Eberhard and Kevin Ford and Dimitris Koukoulopoulos},
title = {Permutations contained in transitive subgroups},
journal = {Discrete analysis},
year = {2016},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DAS_2016_a7/}
}