Geometric permutations for convex sets

@article{Katchalski1985GeometricPF,
  title={Geometric permutations for convex sets},
  author={Meir Katchalski and Ted Lewis and Joseph Zaks},
  journal={Discrete Mathematics},
  year={1985},
  volume={54},
  pages={271-284}
}
Let ~ = { A 1 , . . . , A n } be a family of n pairwise disjoint convex sets in the plane. A common transversal for ~ is a straight line meeting each of the sets. Since the sets are disjoint and convex a common transversal meets the sets in a definite order, up to reversal, and therefore determines a permutation and its 'reverse'. Such a permutation and its 'reverse' are called a geometric permutation or a G.P. for short. Let ~,~ denote the family of all geometric permutations of ~ . We wish to… CONTINUE READING