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.

  Keywords:  Narayana number; Catalan number; Motzkin path; Weighted Motzkin path; Multiple Dyck path; Bijection

   AMS Classification:  05A15, 05A19.
   
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