Bijectives relations between ordered trees and several Lattice paths

摘要

In this paper, we unionized the three Lattice paths, i.e.Dyck path, Motzkin path and Schrfider path, and obtained a new path named k-path by studying their properties. Using the relations between the total numbers of lattice points and Catalan numbers, bijectives relations between ordered trees and several Lattice paths are proposed. It laid foundation for furtherly researching Lattice paths.