# Action Graphs and Catalan Numbers

@article{Alvarez2015ActionGA, title={Action Graphs and Catalan Numbers}, author={Gerardo Alvarez and Julia E. Bergner and Rub{\'e}n L{\'o}pez}, journal={J. Integer Seq.}, year={2015}, volume={18}, pages={15.7.2} }

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 an isomorphism between the set of edges adjoined at step $k$ and the set of planar rooted trees with $k$ edges.

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Action graphs, rooted planar forests, and self-convolutions of the Catalan numbers

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- Involve, a Journal of Mathematics
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We show that families of action graphs, with initial graphs which are linear of varying length, give rise to self-convolutions of the Catalan sequence. We prove this result via a comparison with… Expand

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