Séminaire Lotharingien de Combinatoire, B46b (2001), 14 pp.

Elena Barcucci, Elisa Pergola, Renzo Pinzani and Simone Rinaldi

ECO Method and Hill-free Generalized Motzkin Paths

Abstract. In this paper we study the class of generalized Motzkin paths with no hills and prove some of their combinatorial properties in a bijective way; as a particular case we have the Fine numbers, enumerating Dyck paths with no hills. Using the ECO method, we define a recursive construction for Dyck paths such that the number of local expansions performed on each path depends on the number of its hills. We then extend this construction to the set of generalized Motzkin paths.

Received: April 14, 2001; Accepted: June 1, 2001.

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