Title: Inscribable order types


Abstract:

We call an order type inscribable if it is realized by a point configuration where all extreme points are all on a circle. In this talk, we investigate the 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 Möbius transformations. We also suggest open problems around inscribability. This is a joint work with Michael Gene Dobbins.