English

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

Combinatorics 2023-09-25 v1 Metric Geometry

Abstract

Given a finite set of points CRdC \subseteq \mathbb{R}^d, we say that an ordering of CC is protrusive if every point lies outside the convex hull of the points preceding it. We give an example of a set CC of 55 points in the Euclidean plane possessing a protrusive ordering that cannot be obtained by ranking the points of CC according to the sum of their distances to a finite multiset of points. This answers a question of Alon, Defant, Kravitz and Zhu.

Keywords

Cite

@article{arxiv.2309.12809,
  title  = {A protrusive ordering of 5 points not witnessed by any finite multiset},
  author = {Adrian Beker},
  journal= {arXiv preprint arXiv:2309.12809},
  year   = {2023}
}