{"page":"344 - 349","language":[{"iso":"eng"}],"scopus_import":"1","date_created":"2018-12-11T12:06:56Z","day":"01","status":"public","publication":"Journal of Combinatorial Theory Series A","_id":"4098","publication_status":"published","date_published":"1986-11-01T00:00:00Z","article_processing_charge":"No","month":"11","publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"oa_version":"None","publisher":"Elsevier","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Stöckl, Gerd","first_name":"Gerd","last_name":"Stöckl"}],"doi":"10.1016/0097-3165(86)90075-0","citation":{"mla":"Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite Point-Sets in Euclidean Spaces.” <i>Journal of Combinatorial Theory Series A</i>, vol. 43, no. 2, Elsevier, 1986, pp. 344–49, doi:<a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">10.1016/0097-3165(86)90075-0</a>.","chicago":"Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite Point-Sets in Euclidean Spaces.” <i>Journal of Combinatorial Theory Series A</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">https://doi.org/10.1016/0097-3165(86)90075-0</a>.","short":"H. Edelsbrunner, G. Stöckl, Journal of Combinatorial Theory Series A 43 (1986) 344–349.","ista":"Edelsbrunner H, Stöckl G. 1986. The number of extreme pairs of finite point-sets in Euclidean spaces. Journal of Combinatorial Theory Series A. 43(2), 344–349.","ieee":"H. Edelsbrunner and G. Stöckl, “The number of extreme pairs of finite point-sets in Euclidean spaces,” <i>Journal of Combinatorial Theory Series A</i>, vol. 43, no. 2. Elsevier, pp. 344–349, 1986.","ama":"Edelsbrunner H, Stöckl G. The number of extreme pairs of finite point-sets in Euclidean spaces. <i>Journal of Combinatorial Theory Series A</i>. 1986;43(2):344-349. doi:<a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">10.1016/0097-3165(86)90075-0</a>","apa":"Edelsbrunner, H., &#38; Stöckl, G. (1986). The number of extreme pairs of finite point-sets in Euclidean spaces. <i>Journal of Combinatorial Theory Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">https://doi.org/10.1016/0097-3165(86)90075-0</a>"},"article_type":"original","extern":"1","intvolume":"        43","type":"journal_article","title":"The number of extreme pairs of finite point-sets in Euclidean spaces","publist_id":"2020","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0097316586900750?via%3Dihub","open_access":"1"}],"date_updated":"2022-02-01T14:02:41Z","oa":1,"volume":43,"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","year":"1986","issue":"2","abstract":[{"text":"To points p and q of a finite set S in d-dimensional Euclidean space Ed are extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum number of extreme pairs realized by any n points in Ed. We give geometric proofs of , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since all other cases are trivial.","lang":"eng"}],"quality_controlled":"1"}