Year: 2024
Type: article
Abstract: We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a bijection proving this fact. Rushed paths turn out to be in bijection with one-sided trees, introduced by Durhuus and Unel, which have an asymptotic enumeration involving a stretched exponential. We conclude by presenting several other classes of related lattice paths and directed animals that may have similar asymptotic properties.
DOI: 10.4204/eptcs.403.10
Author: Axel Bacher
Institution: Université Sorbonne Paris Nord
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4392822295