Action graphs and Catalan numbers

Published 28 Feb 2015 in math.CO | (1503.00044v2)

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 $k$th Catalan number. Furthermore, we establish an isomorphism between the set of edges adjoined at step $k$ and the set of planar rooted trees with $k$ edges.

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