Cycle Lengths in a Permutation are Typically Poisson

Andrew Granville
2006 Electronic Journal of Combinatorics  
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 fatcat:6gevmk5bnrhalhcqsfhmfqebia