Geodesic
Three-Dimensional Catalan Numbers and Product-Coproduct Prographs
Séminaire lotharingien de combinatoire, 78B (2017) 
Nicolas Borie. Three-Dimensional Catalan Numbers and Product-Coproduct Prographs. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a38/
@article{SLC_2017_78B_a38,
     author = {Nicolas Borie},
     title = {Three-Dimensional {Catalan} {Numbers} and {Product-Coproduct} {Prographs}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2017},
     volume = {78B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a38/}
}
TY  - JOUR
AU  - Nicolas Borie
TI  - Three-Dimensional Catalan Numbers and Product-Coproduct Prographs
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a38/
ID  - SLC_2017_78B_a38
ER  - 
%0 Journal Article
%A Nicolas Borie
%T Three-Dimensional Catalan Numbers and Product-Coproduct Prographs
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a38/
%F SLC_2017_78B_a38

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We present the new combinatorial class of product-coproduct prographs which are planar assemblies of two types of operators: products having two inputs and a single output and coproducts having a single input and two outputs. We show that such graphs are enumerated by the 3-dimensional Catalan numbers. We present some combinatorial bijections positioning product-coproduct prographs as key objects to probe families of objects enumerated by the 3-dimensional Catalan numbers.