Geodesic
Permutations contained in transitive subgroups
Discrete analysis (2016) Cet article a éte moissonné depuis la source Scholastica

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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 $\mathcal{A}_n$.
Publié le : 
@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/}
}
TY  - JOUR
AU  - Sean Eberhard
AU  - Kevin Ford
AU  - Dimitris Koukoulopoulos
TI  - Permutations contained in transitive subgroups
JO  - Discrete analysis
PY  - 2016
UR  - http://geodesic.mathdoc.fr/item/DAS_2016_a7/
LA  - en
ID  - DAS_2016_a7
ER  - 
%0 Journal Article
%A Sean Eberhard
%A Kevin Ford
%A Dimitris Koukoulopoulos
%T Permutations contained in transitive subgroups
%J Discrete analysis
%D 2016
%U http://geodesic.mathdoc.fr/item/DAS_2016_a7/
%G en
%F DAS_2016_a7
Sean Eberhard; Kevin Ford; Dimitris Koukoulopoulos. Permutations contained in transitive subgroups. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a7/