Abstract :
An elementary technique is used for the enumeration of Dyck paths according to various parameters. For several of the considered parameters the generating function is expressed in terms of the Narayana function. Many enumeration results are obtained, some of which involve the Fine numbers.
Keywords :
Dyck paths , Combinatorial enumeration , Generating functions , Catalan numbers , Fine numbers , Narayana numbers , Similarity relations , Ordered trees , Non-crossing partitions , Parallelogram polyominoes
