{"title":"Peeling Sequences","authors":"Adrian Dumitrescu, Géza Tóth","doi":"10.1007/s00454-023-00616-8","DOIUrl":null,"url":null,"abstract":"<p>Given a set of <i>n</i> 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 <i>n</i>! ways, which is the maximum number of ways for <i>n</i> points. But what is the minimum number? It is shown that this number is (roughly) at least <span>\\(3^n\\)</span> and at most <span>\\(12.29^n\\)</span>.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"24 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete & Computational Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00454-023-00616-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
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Abstract
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 \(3^n\) and at most \(12.29^n\).
给定平面内一般位置的 n 个标记点集合，我们逐个删除其所有点。每移去一个点，就会从剩余集合的凸壳中移除一个点。这个过程有多少种方式？答案显然取决于点集。如果点都在凸面位置，那么正好有 n 种方法，这是 n 个点的最大方法数。那么最小的路数是多少呢？结果表明，这个数目（大致）至少是（3^n\），最多是（12.29^n\）。
期刊介绍：
Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.
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