Progressive and Rushed Dyck Paths
Combinatorics
2026-05-25 v5 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.2403.08120,
title = {Progressive and Rushed Dyck Paths},
author = {Axel Bacher},
journal= {arXiv preprint arXiv:2403.08120},
year = {2026}
}
Comments
In Proceedings GASCom 2024, arXiv:2406.14588