Pamela E. Harris ; J. Carlos Martínez Mori ; Alexander N. Wilson - A Pollak Proof for the Number of Weakly Increasing Parking Functions

dmtcs:17006 - Discrete Mathematics & Theoretical Computer Science, April 10, 2026, vol. 28:1, Permutation Patterns 2025 - https://doi.org/10.46298/dmtcs.17006
A Pollak Proof for the Number of Weakly Increasing Parking FunctionsArticle

Authors: Pamela E. Harris ; J. Carlos Martínez Mori ; Alexander N. Wilson

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.


Volume: vol. 28:1, Permutation Patterns 2025
Section: Special issues
Published on: April 10, 2026
Accepted on: April 7, 2026
Submitted on: December 1, 2025
Keywords: Combinatorics, 05A15