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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