Papers › A protrusive ordering of 5 points not witnessed by any finite multiset
A protrusive ordering of 5 points not witnessed by any finite multiset
Adrian Beker
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Given a finite set of points C ⊆ℝᵈ, 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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