Counting triangulations of some classes of subdivided convex polygons
Autor: | Asinowski, Andrei, Krattenthaler, Christian, Mansour, Toufik |
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Rok vydání: | 2016 |
Předmět: | |
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 |
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