Counting triangulations of some classes of subdivided convex polygons

Autor:	Asinowski, Andrei, Krattenthaler, Christian, Mansour, Toufik
Rok vydání:	2016
Předmět:	Mathematics - Combinatorics Computer Science - Computational Geometry 05A10 05A15 05A16
Zdroj:	Europ. J. Combin. 62 (2017), 92-114
Druh dokumentu:	Working Paper
Popis:	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. Comment: 26 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1604.02870 Zobrazit plný text záznamu View this record from Arxiv