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@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} }

- Published 1985 in Discrete Mathematics
DOI:10.1016/0012-365X(85)90111-6

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

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