\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 Evangelos Georgiadis, David Callan and Qing-Hu Hou}
%
%
\medskip
\noindent
%
%
{\bf Circular Digraph Walks, $k$-Balanced Strings, Lattice Paths and Chebychev Polynomials}
%
%
\vskip 5mm
\noindent
%
%
%
%
We count the number of walks of length $n$ on a $k$-node circular
digraph that cover all $k$ nodes in two ways. The first way
illustrates the transfer-matrix method. The second involves counting
various classes of height-restricted lattice paths.  We observe that
the results also count so-called $k$-balanced strings of length $n$,
generalizing a 1996 Putnam problem.



\bye

.