Action Graphs and Catalan Numbers
Gerardo Alvarez, Julia E. Bergner, and Ruben Lopez
Department of Mathematics
University of California, Riverside
Riverside, CA 92521
USA
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 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,
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(Concerned with sequences
A000108
A014137.)
Received March 2 2015;
revised versions received June 12 2015; June 25 2015.
Published in Journal of Integer Sequences, June 30 2015.
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