Journal of Integer Sequences, Vol. 18 (2015), Article 15.7.2

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.

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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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