The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2
Herbert Edelsbrunner
Sharir, Micha
LetS be a collection ofn convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 ton. A pair of permutations
(i1i2in−1in)(inin−1i2i1)
is called ageometric permutation of S if there is a line that intersects all sets ofS in this order. We prove thatS can realize at most 2n–2 geometric permutations. This upper bound is tight.
Springer
1990
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https://research-explorer.app.ist.ac.at/record/4068
Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. <i>Discrete & Computational Geometry</i>. 1990;5(1):35-42. doi:<a href="https://doi.org/ 10.1007/BF02187778"> 10.1007/BF02187778</a>
info:eu-repo/semantics/altIdentifier/doi/ 10.1007/BF02187778
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