Geodesic
Action graphs and Catalan numbers
Journal of integer sequences, Tome 18 (2015) no. 7
We introduce an inductively defined sequence of directed graphs and prove that the number of edges added at step $k$ is equal to the $k$th Catalan number. Furthermore, we establish a bijection between the set of edges adjoined at step $k$ and the set of planar rooted trees with $k$ edges.
Classification : 05A19, 05C05
Keywords: Catalan number, directed graph 
@article{JIS_2015__18_7_a6,
     author = {Alvarez,  Gerardo and Bergner,  Julia E. and Lopez,  Ruben},
     title = {Action graphs and {Catalan} numbers},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {7},
     zbl = {1327.05029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a6/}
}
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AU  - Bergner,  Julia E.
AU  - Lopez,  Ruben
TI  - Action graphs and Catalan numbers
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a6/
LA  - en
ID  - JIS_2015__18_7_a6
ER  - 
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%A Bergner,  Julia E.
%A Lopez,  Ruben
%T Action graphs and Catalan numbers
%J Journal of integer sequences
%D 2015
%V 18
%N 7
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a6/
%G en
%F JIS_2015__18_7_a6
Alvarez,  Gerardo; Bergner,  Julia E.; Lopez,  Ruben. Action graphs and Catalan numbers. Journal of integer sequences, Tome 18 (2015) no. 7. http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a6/