\magnification=1200
\hsize=4in
\nopagenumbers
\noindent
%
%
{\bf Nicolas Pouyanne  }
%
%
\medskip
\noindent
%
%
{\bf On the Number of Permutations Admitting an m-th Root}
%
%
\vskip 5mm
\noindent
%
%
%
%
Let $m$ be a positive integer, and $p_n(m)$ the proportion of
permutations of the symmetric group $S_n$ that admit an $m$-th root.
Calculating the exponential generating function of these permutations, we
show the following asymptotic formula
$$p_n(m)\, \sim \, 
 {{\pi _m}\over {n^{1-\varphi (m)/m}}},\;\; n\to \infty ,$$
where $\varphi$ is the Euler function and $\pi _m$ an explicit
constant.

\bye

.
