Action graphs and Catalan numbers

Abstract

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.

7 pages; minor changes from original draft. arXiv admin note: text overlap with arXiv:1807.03005

Cited by in corpus (1)

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