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arXiv · 1210.3349

The central component of a triangulation

Alon Regev
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Abstract

The central component of a polygon triangulation is defined as the triangle or diameter that contain its geometric center. More generally, every polygon dissection contains a central component. Using this notion, we derive new recurrences for the Catalan and $k$-Catalan numbers, and use these recursions to prove congruence relations of these numbers. We also enumerate the triangulations that contain a fixed vertex in their central components.

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Alon Regev. 2012-10-11. The central component of a triangulation. https://arxiv.org/abs/1210.3349

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