Geodesic
ECO Method and Hill-free Generalized Motzkin Paths
Séminaire lotharingien de combinatoire, Tome 46 (2001-2002) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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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. 

@article{SLC_2001-2002_46_a1,
     author = {Elena Barcucci and Elisa Pergola and Renzo Pinzani and Simone Rinaldi},
     title = {ECO {Method} and {Hill-free} {Generalized} {Motzkin} {Paths}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2001-2002},
     volume = {46},
     url = {http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a1/}
}
TY  - JOUR
AU  - Elena Barcucci
AU  - Elisa Pergola
AU  - Renzo Pinzani
AU  - Simone Rinaldi
TI  - ECO Method and Hill-free Generalized Motzkin Paths
JO  - Séminaire lotharingien de combinatoire
PY  - 2001-2002
VL  - 46
UR  - http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a1/
ID  - SLC_2001-2002_46_a1
ER  - 
%0 Journal Article
%A Elena Barcucci
%A Elisa Pergola
%A Renzo Pinzani
%A Simone Rinaldi
%T ECO Method and Hill-free Generalized Motzkin Paths
%J Séminaire lotharingien de combinatoire
%D 2001-2002
%V 46
%U http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a1/
%F SLC_2001-2002_46_a1
Elena Barcucci; Elisa Pergola; Renzo Pinzani; Simone Rinaldi. ECO Method and Hill-free Generalized Motzkin Paths. Séminaire lotharingien de combinatoire, Tome 46 (2001-2002). http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a1/