Abstract
The probability that a random pair of elements from the alternating group $A_{n}$ generates all of $A_{n}$ is shown to have an asymptotic expansion of the form $1-1/n-1/n^{2}-4/n^{3}-23/n^{4}-171/n^{5}-... $. This same asymptotic expansion is valid for the probability that a random pair of elements from the symmetric group $S_{n}$ generates either $A_{n}$ or $S_{n}$. Similar results hold for the case of $r$ generators ($r>2$).
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
9 articles.
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