[{"type":"journal_article","publisher":"Springer","title":"The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2","volume":5,"date_updated":"2019-04-26T07:22:39Z","publication":"Discrete & Computational Geometry","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\n(i1i2in−1in)(inin−1i2i1) \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."}],"date_created":"2018-12-11T12:06:45Z","page":"35 - 42","intvolume":" 5","doi":" 10.1007/BF02187778","status":"public","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Herbert Edelsbrunner","last_name":"Edelsbrunner"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"}],"citation":{"mla":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” *Discrete & Computational Geometry*, vol. 5, no. 1, Springer, 1990, pp. 35–42, doi: 10.1007/BF02187778.","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” *Discrete & Computational Geometry* 5, no. 1 (1990): 35–42. https://doi.org/ 10.1007/BF02187778.","ista":"Edelsbrunner H, Sharir M. 1990. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry. 5(1), 35–42.","short":"H. Edelsbrunner, M. Sharir, Discrete & Computational Geometry 5 (1990) 35–42.","apa":"Edelsbrunner, H., & Sharir, M. (1990). The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. *Discrete & Computational Geometry*, *5*(1), 35–42. https://doi.org/ 10.1007/BF02187778","ieee":"H. Edelsbrunner and M. Sharir, “The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2,” *Discrete & Computational Geometry*, vol. 5, no. 1, pp. 35–42, 1990.","ama":"Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. *Discrete & Computational Geometry*. 1990;5(1):35-42. doi: 10.1007/BF02187778"},"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.","publication_status":"published","year":"1990","publist_id":"2057","date_published":"1990-01-01T00:00:00Z","_id":"4068","quality_controlled":0,"day":"01","extern":1,"month":"01"}]