任何有限多集都无法见证的 5 点突出排序

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-06-20 DOI:10.1007/s00013-024-02020-x

Adrian Beker

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引用次数: 0

摘要

给定一个有限点集 C（C 的子集{\mathbb {R}}^d\ ），如果每个点都位于它前面的点的凸壳之外，我们就说 C 的排序是突出的。我们举例说明，欧几里得平面上一个由 5 个点组成的集合 C 拥有一个突出排序，而这个突出排序无法通过将 C 中的点按照它们到一个有限多点集合的距离之和进行排序来获得。这回答了 Alon、Defant、Kravitz 和 Zhu 的一个问题。

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A protrusive ordering of 5 points not witnessed by any finite multiset

Given a finite set of points \(C \subseteq {\mathbb {R}}^d\), we say that an ordering of C is protrusive if every point lies outside the convex hull of the points preceding it. We give an example of a set C of 5 points in the Euclidean plane possessing a protrusive ordering that cannot be obtained by ranking the points of C according to the sum of their distances to a finite multiset of points. This answers a question of Alon, Defant, Kravitz, and Zhu.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.