2022/11/11 by Adrian Dumitrescu, Dumitrescu, Adrian, Tóth, Géza · 1 citation
Computer Science · Engineering · Mathematics · #Architecture and Computational Design #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2211.05968
openalex publication_date 2022/11/11 · openalex created_date 2022/11/21 · openalex updated_date 2026/07/28
Given a set of n labeled points in general position in the plane, we remove all of its points one by one. At each step, one point from the convex hull of the remaining set is erased. In how many ways can the process be carried out? The answer obviously depends on the point set. If the points are in convex position, there are exactly n! ways, which is the maximum number of ways for n points. But what is the minimum number? It is shown that this number is (roughly) at least 3n and at most 12.29n.