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arXiv · 2206.01253

Inscribable order types

Michael Gene Dobbins·Seunghun Lee
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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 $\Theta(\frac{4^n}{n^{3/2}})$. We further construct an infinite family of minimally uninscribable order types. The proof of uninscribability mainly uses M\"obius transformations. We also suggest open problems around inscribability.

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Michael Gene Dobbins, Seunghun Lee. 2022-06-02. Inscribable order types. https://arxiv.org/abs/2206.01253

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