article The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2 published Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Micha Sharir author 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. Springer1990 Discrete & Computational Geometry 10.1007/BF02187778 5135 - 42 yes H. Edelsbrunner, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 35–42. Edelsbrunner, H., &#38; Sharir, M. (1990). The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. <i>Discrete &#38; Computational Geometry</i>, <i>5</i>(1), 35–42. <a href="https://doi.org/ 10.1007/BF02187778">https://doi.org/ 10.1007/BF02187778</a> Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. <i>Discrete &#38; Computational Geometry</i>. 1990;5(1):35-42. doi:<a href="https://doi.org/ 10.1007/BF02187778"> 10.1007/BF02187778</a> H. Edelsbrunner and M. Sharir, “The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2,” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, pp. 35–42, 1990. Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” <i>Discrete &#38; Computational Geometry</i> 5, no. 1 (1990): 35–42. <a href="https://doi.org/ 10.1007/BF02187778">https://doi.org/ 10.1007/BF02187778</a>. Edelsbrunner H, Sharir M. 1990. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete &#38; Computational Geometry. 5(1), 35–42. Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, Springer, 1990, pp. 35–42, doi:<a href="https://doi.org/ 10.1007/BF02187778"> 10.1007/BF02187778</a>. 40682018-12-11T12:06:45Z2019-04-26T07:22:39Z