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

2023/09/22 by Adrian Beker, Beker, Adrian
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2309.12809

openalex publication_date 2023/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite set of points C ⊆ 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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