Local probabilities for random permutations without long cycles
Combinatorics
2015-01-05 v1 Probability
Abstract
We explore the probability that a permutation sampled from the symmetric group of order n uniformly at random has cycles of lengths not exceeding r. Asymptotic formulas valid in specified regions for the ratio n/r are obtained using the saddle point method combined with ideas originated in analytic number theory. Theorem 1 and its detailed proof are included to rectify formulas for small r which have been announced by a few other authors.
Cite
@article{arxiv.1501.00136,
title = {Local probabilities for random permutations without long cycles},
author = {Eugenijus Manstavičius and Robertas Petuchovas},
journal= {arXiv preprint arXiv:1501.00136},
year = {2015}
}
Comments
25 pages