Inscribable order types
Metric Geometry
2023-10-30 v2
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 . 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.
Cite
@article{arxiv.2206.01253,
title = {Inscribable order types},
author = {Michael Gene Dobbins and Seunghun Lee},
journal= {arXiv preprint arXiv:2206.01253},
year = {2023}
}