Geodesic
Asymptotics of generating the symmetric and alternating groups.
The electronic journal of combinatorics, Tome 12 (2005)

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Zbl EuDML
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 ($r>2$).
DOI : 10.37236/1953
Classification : 20P05, 20B30, 20F05, 05A16
Mots-clés : random pairs of elements, alternating groups, asymptotic expansions, symmetric groups 
John D. Dixon. Asymptotics of generating the symmetric and alternating groups.. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1953
@article{10_37236_1953,
     author = {John D. Dixon},
     title = {Asymptotics of generating the symmetric and alternating groups.},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1953},
     zbl = {1086.20045},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1953/}
}
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