Abstract
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.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Multiplicative arithmetic functions and the generalized Ewens measure;Israel Journal of Mathematics;2024-04-24
2. Most permutations power to a cycle of small prime length;Proceedings of the Edinburgh Mathematical Society;2021-05
3. Analytic number theory for 0-cycles;Mathematical Proceedings of the Cambridge Philosophical Society;2017-10-30
4. Four random permutations conjugated by an adversary generateSnwith high probability;Random Structures & Algorithms;2015-12-24
5. Permutations Fixing ak-set;International Mathematics Research Notices;2015-12-23