Geodesic
Cycle lengths in a permutation are typically Poisson
The electronic journal of combinatorics, Tome 13 (2006)
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The set of cycle lengths of almost all permutations in $S_n$ are "Poisson distributed": we show that this remains true even when we restrict the number of cycles in the permutation. The formulas we develop allow us to also show that almost all permutations with a given number of cycles have a certain "normal order" (in the spirit of the Erdős-Turán theorem). Our results were inspired by analogous questions about the size of the prime divisors of "typical" integers.
DOI : 10.37236/1133
Classification : 05A05, 60C05 
@article{10_37236_1133,
     author = {Andrew Granville},
     title = {Cycle lengths in a permutation are typically {Poisson}},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1133},
     zbl = {1171.05001},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1133/}
}
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%A Andrew Granville
%T Cycle lengths in a permutation are typically Poisson
%J The electronic journal of combinatorics
%D 2006
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Andrew Granville. Cycle lengths in a permutation are typically Poisson. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1133

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