Fixed points and cycles of parking functions

Martin Rubey, Mei Yin

A parking function of length $n$ is a sequence $\pi =({\pi }_1,\dots ,{\pi }_n)$ of positive integers such that if ${\lambda }_1\le \cdots \le {\lambda }_n$ is the increasing rearrangement of ${\pi }_1,\dots ,{\pi }_n$, th…