Inscribable order types

2022/06/02 by Dobbins, Michael Gene, Lee, Seunghun
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2206.01253

Abstract

We call an order type inscribable if it is realized by a point configuration where the extreme points are all on a circle. In this paper, we investigate inscribability of order types. We first show that every simple order type with at most 2 interior points is inscribable, and that the number of such order types is Θ(\frac4ⁿn^3/2). We further construct an infinite family of minimally uninscribable order types. The proof of uninscribability mainly uses Möbius transformations. We also suggest open problems around inscribability.

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