Action Graphs and Catalan Numbers
Gerardo Alvarez, Julia E. Bergner, and Ruben Lopez
Department of Mathematics
University of California, Riverside
Riverside, CA 92521
We introduce an inductively defined sequence of directed graphs and
prove that the number of edges added at step k is equal to the kth
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.
Full version: pdf,
(Concerned with sequences
Received March 2 2015;
revised versions received June 12 2015; June 25 2015.
Published in Journal of Integer Sequences, June 30 2015.
Journal of Integer Sequences home page