A Pollak Proof for the Number of Weakly Increasing Parking Functions

Abstract

We develop a circular-street argument, in the style of Pollak, to obtain a new proof that there are $C_n=\frac{1}{n+1}\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$ weakly increasing parking functions of length $n\ge 1$, where $C_n$ is the $n$th Catalan number.