\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Stephan G. Wagner}
%
%
\medskip
\noindent
%
%
{\bf On an Identity for the Cycle Indices of Rooted Tree Automorphism Groups}
%
%
\vskip 5mm
\noindent
%
%
%
%
This note deals with a formula due to G. Labelle for the summed cycle
indices of all rooted trees, which resembles the well-known formula
for the cycle index of the symmetric group in some way. An elementary
proof is provided as well as some immediate corollaries and
applications, in particular a new application to the enumeration of
$k$-decomposable trees. A tree is called $k$-decomposable in this
context if it has a spanning forest whose components are all of size
$k$.
\bye