### Quantitative Steinitz theorems

Naszodi Marton#### BBC+G Seminar

on 3/17/23

Given an -element point set in the plane, in how many ways can it be peeled off until no point remains? Only one extreme point can be removed at a time. The answer obviously depends on the point set. If the points are in convex position, there are exactly ways, which is the maximum number of ways for points. But what is the minimum number? After failing to obtain a good estimate, we examine how the above removal procedure may reveal information about the distance from convexity of a given point set. We look at other methods as well.