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arXiv · 1604.02870

Counting triangulations of some classes of subdivided convex polygons

Andrei Asinowski·Christian Krattenthaler·Toufik Mansour
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Abstract

We compute the number of triangulations of a convex $k$-gon each of whose sides is subdivided by $r-1$ points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as $k$ and/or $r$ tend to infinity. We connect these results with the question of finding the planar set of points in general position that has the minimum possible number of triangulations - a well-known open problem from computational geometry.

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Andrei Asinowski, Christian Krattenthaler, Toufik Mansour. 2016-04-11. Counting triangulations of some classes of subdivided convex polygons. https://arxiv.org/abs/1604.02870

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