Counting triangulations and pseudo-triangulations of wheels
نویسندگان
چکیده
Motivated by several open questions on triangulations and pseudotriangulations, we give closed form expressions for the number of triangulations and the number of minimum pseudo-triangulations of n points in wheel configurations, that is, with n − 1 in convex position. Although the numbers of triangulations and pseudotriangulations vary depending on the placement of the interior point, their difference is always the (n−2)nd Catalan number. We also prove an inequality #PT ≤ 3#T for the numbers of minimum pseudo-triangulations and triangulations of any point configuration with i interior
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A Simple Sweep Line Algorithm for Counting Triangulations and Pseudo-triangulations
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