Geodesic
The average order of a permutation
The electronic journal of combinatorics, Tome 5 (1998)
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We show that the average order $\mu_n$ of a permutation in $S_n$ satisfies $$ \log\mu_n\ =\ C\sqrt{\frac n{\log n}} + O\left(\frac{\sqrt n\log\log n}{\log n}\right), $$ which refines earlier results of Erdős and Turán, Schmutz, and Goh and Schmutz.
DOI : 10.37236/1379
Classification : 11N45, 20B30, 05A05, 11P82, 11N37, 20P05
Mots-clés : asymptotic formula for the expected order of a random permutation, symmetric group 
@article{10_37236_1379,
     author = {Richard Stong},
     title = {The average order of a permutation},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1379},
     zbl = {0907.11031},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1379/}
}
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Richard Stong. The average order of a permutation. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1379

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