Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.1

The Central Component of a Triangulation

Alon Regev
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL 60115


We define the central component of a triangulation of a regular convex polygon as the diameter or triangle containing its geometric center. This definition yields a new recursion relation for Catalan numbers, which can be used to derive congruence relations. We generalize this idea to k-angulations, giving congruences of k-Catalan numbers. We also enumerate the triangulations that include a fixed vertex in their central components.

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(Concerned with sequence A000108 A027302 A137211.)

Received October 21 2012; revised version received March 1 2013. Published in Journal of Integer Sequences, March 9 2013.

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