Progressive and Rushed Dyck Paths
<|reference_start|>Progressive and Rushed Dyck Paths: 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.<|reference_end|>
@article{bacher2024progressive,
    title={Progressive and Rushed Dyck Paths},
    author={Axel Bacher (Universite Sorbonne Paris Nord)},
    journal={EPTCS 403, 2024, pp. 29-34},
    year={2024},
    doi={10.4204/EPTCS.403.10},
    archivePrefix={arXiv},
    eprint={2403.08120},
    primaryClass={math.CO cs.DM}
}