{"month":"01","year":"1990","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"title":"The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2","quality_controlled":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187778"}],"intvolume":"         5","extern":"1","date_published":"1990-01-01T00:00:00Z","citation":{"mla":"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>.","short":"H. Edelsbrunner, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 35–42.","ama":"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>","ieee":"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. Springer, pp. 35–42, 1990.","chicago":"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>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02187778\">https://doi.org/10.1007/BF02187778</a>.","apa":"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>. Springer. <a href=\"https://doi.org/10.1007/BF02187778\">https://doi.org/10.1007/BF02187778</a>","ista":"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."},"page":"35 - 42","doi":"10.1007/BF02187778","type":"journal_article","article_type":"original","issue":"1","acknowledgement":"Research of the first author was supported by Amoco Foundation for Faculty Development in Computer Science Grant No. 1-6-44862. Work on this paper by the second author was supported by Office of Naval Research Grant No. N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation and the IBM Corporation.","status":"public","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"}],"oa_version":"None","date_updated":"2022-02-22T14:50:34Z","publist_id":"2057","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_processing_charge":"No","publisher":"Springer","day":"01","_id":"4068","publication_status":"published","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","date_created":"2018-12-11T12:06:45Z","abstract":[{"lang":"eng","text":"LetS be a collection ofn convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 ton. A pair of permutations\r\n(i1i2in−1in)(inin−1i2i1) \r\nis 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."}],"volume":5}