  A parking function of length $n$ is a sequence $\pi=(\pi_1,\dots, \pi_n)$ of
positive integers such that if $\lambda_1\leq\cdots\leq \lambda_n$ is the
increasing rearrangement of $\pi_1,\dots,\pi_n$, then $\lambda_i\leq i$ for
$1\leq i\leq n$. In this paper we obtain some exact results on the number of
fixed points and cycles of parking functions. Our proofs will be based on
generalizations of Pollak's argument. Extensions of our techniques are
discussed.
