Combinatorics of the zeta map on rational Dyck paths

Cesar Ceballos, Tom Denton, Christopher R. H. Hanusa

An $(a,b)$-Dyck path $P$ is a lattice path from $(0,0)$ to $(b,a)$ that stays above the line $y=\frac{a}{b}x$. The zeta map is a curious rule that maps the set of $(a,b)$-Dyck path…