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