Geodesic
Action graphs and Catalan numbers
Journal of integer sequences, Tome 18 (2015) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {18},
     number = {7},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a6/}
}
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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/