THE MAXIMUM NUMBER OF WAYS TO STAB N-CONVEX NONINTERSECTING SETS IN THE PLANE IS 2N-2

Let S be a collection of n convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 to n. A pair of permutations {Mathematical expression} is called a geometric permutation of S if there is a line that intersects all sets of S in this order. We prove that S can realize at most 2 n-2 geometric permutations. This upper bound is tight. © 1990 Springer-Verlag New York Inc.