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Math 192r, Problem Set \#13 \\
(due 11/8/01)
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\begin{enumerate}
\item
\begin{itemize}
\item[(a)]
How many lattice paths from $(0,0)$ to $(m,n)$
remain the same when you rotate them by 180 degrees 
about $(\frac{m}{2},\frac{n}{2})$?
Prove your answer.
\end{itemize}
\item
\begin{itemize}
\item[(a)]
How many lattice paths from $(0,0)$ to $(n,n)$
remain the same when you flip them across the diagonal 
joining $(n,0)$ and $(0,n)$?
Prove your answer.
\item[(b)]
What is the sum of the $q$-weights of these lattice paths?
Conjecture an answer.
\item[(c)]
Why is there no part (b) for question 1?
\end{itemize}
\end{enumerate}
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