New Formulas for Dyck Paths in a Rectangle

Abstract

We consider the problem of counting the set of D a,b of Dyck paths inscribed in a rectangle of size a × b. They are a natural generalization of the classical Dyck words enumerated by the Catalan numbers. By using Ferrers diagrams associated to Dyck paths, we derive formulas for the enumeration of D a,b with a and b non relatively prime, in terms of Catalan numbers.