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.

翻译：渐进路径与急促路径是由Asinowski和Jelinek研究的两类Dyck路径族，它们具有相同的枚举序列（OEIS条目A287709）。我们通过构建双射证明这一事实。研究发现急促路径与Durhuus和Unel提出的单侧树存在双射关系，后者的渐近枚举涉及拉伸指数函数。最后，我们提出了其他几类可能具有类似渐近性质的格路径与有向动物模型。