Meanders and Dyck-Path Billiards

Sen-Peng Eu, Tung-Shan Fu, Hsiang-Chun Hsu

We study a statistic $\mathsf{traj}$ on the ordered pairs $(P,Q)$ of Dyck paths of size $n$, which counts the number of billiard trajectories in the grid polygon enclosed by $P$ an…