English

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 kk is equal to the kkth Catalan number. Furthermore, we establish an isomorphism between the set of edges adjoined at step kk and the set of planar rooted trees with kk 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

R2 v1 2026-06-22T08:40:17.187Z