Adrian Dumitrescu: Peeling Sequences

Given an $n$-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 $n!$ ways, which is the maximum number of ways for $n$ 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.