A Pollak Proof for the Number of Weakly Increasing Parking Functions
Pamela E. Harris (1), J. Carlos Martínez Mori (2), Alexander N. Wilson (3)
(1) University of Wisconsin–Milwaukee [UWM]
(2) University of Colorado Denver [UCD]
(3) York University
Abstract
We develop a circular-street argument, in the style of Pollak, to obtain a new proof that there are $C_n = \frac{1}{n+1}\binom{2n}{n}$ weakly increasing parking functions of length $n \geq 1$, where $C_n$ is the $n$th Catalan number.