Year: 2026
Type: preprint
Abstract: Pattern avoidance is a central topic in the study of permutations. Parking functions provide a natural setting in which to ask analogous questions. In this paper, we study parking functions whose parking permutations avoid the patterns $1234$ and $2134$, obtaining an analog of the Schröder numbers for parking functions. To enumerate these objects, we develop an enumeration scheme that runs in polynomial time and adapt the prefix-based framework introduced by Zeilberger in 1998, and later improved by Vatter, by instead using ``suffixes.''
Source: arXiv (Cornell University)
Authors: Martinez, Lucy, Zeilberger, Doron
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214379896