Identities from Weighted Motzkin Paths
William Y.C. Chen, Sherry H.F. Yan and Laura L.M. Yang
Abstract: Based on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we find combinatorial interpretations of two identities related to the Narayana polynomials and the Catalan numbers. These interpretations answer two problems posed recently by Coker.
AMS Classification: 05A15, 05A19
Keywords: Narayana number, Catalan number, Motzkin path, Weighted Motzkin path, Multiple Dyck path, Bijection