On the number of mth roots of permutations
Combinatorics
2012-01-26 v4
Abstract
Let m be a fixed positive integer. It is well-known that a permutation may have one, many, or no mth roots. In this note we provide an explicit expression and a generating function for the number of mth roots of \sigma. Let p_m(n) be the probability that a random n-permutation has an mth root. We also include a proof that p_m(jq)=p_m(jq+1)=... =p_m(jq+(q-1)) where j=0,1,... and m is a power of prime q.
Cite
@article{arxiv.1005.1531,
title = {On the number of mth roots of permutations},
author = {Jesús Leaños and Rutilo Moreno and Luis Manuel Rivera-Martínez},
journal= {arXiv preprint arXiv:1005.1531},
year = {2012}
}
Comments
16 pages. Revised version, one subsection added. To appear in Australas J. Combinatorics