of lattice paths of a certain kind. This occurs when the lattice paths are in bijection with the object in question. For example,

* Dyck paths are counted by the Catalan number . A Dyck path is a lattice path in from to with steps in that never passes below the -axis. Equivalently, a Dyck path is a NE lattice path from to that lies strictly below (but may touch) the diagonal .
* The Schröder numbers