Counting Triangulations of Some Classes
نویسندگان
چکیده
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.
منابع مشابه
Counting triangulations of some classes of subdivided convex polygons
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 triangul...
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