Cycle lengths in a permutation are typically Poisson
type: Item
instance of: scholarly article
title: Cycle lengths in a permutation are typically Poisson
zbMATH Open document ID: 1171.05001
published in: The Electronic Journal of Combinatorics
publication date: 2007-03-12T00:00:00Z
full work available at URL: https://eudml.org/doc/130550
full work available at URL: v13i1r107.html
review text: Summary: 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.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 5132820
author: Andrew Granville
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5132820