Action graphs and Catalan numbers
Combinatorics
2020-02-21 v2
Abstract
We introduce an inductively defined sequence of directed graphs and prove that the number of edges added at step is equal to the th Catalan number. Furthermore, we establish an isomorphism between the set of edges adjoined at step and the set of planar rooted trees with edges.
Keywords
Cite
@article{arxiv.1503.00044,
title = {Action graphs and Catalan numbers},
author = {Gerardo Alvarez and Julia E. Bergner and Ruben Lopez},
journal= {arXiv preprint arXiv:1503.00044},
year = {2020}
}
Comments
7 pages; minor changes from original draft. arXiv admin note: text overlap with arXiv:1807.03005