How often is a permutation an n'th power?
Abstract
We give a short argument that for any fixed n, the probability that a permutation on m letters is an n'th power is asymptotically C m^{phi(n)/n  1}.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.math/9712223
 arXiv:
 arXiv:math/9712223
 Bibcode:
 1997math.....12223L
 Keywords:

 Combinatorics
 EPrint:
 2 pages