{"_id":"4098","publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Stöckl","full_name":"Stöckl, Gerd","first_name":"Gerd"}],"extern":"1","intvolume":"        43","quality_controlled":"1","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0097316586900750?via%3Dihub","open_access":"1"}],"publication_status":"published","page":"344 - 349","article_processing_charge":"No","doi":"10.1016/0097-3165(86)90075-0","title":"The number of extreme pairs of finite point-sets in Euclidean spaces","month":"11","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","oa":1,"date_created":"2018-12-11T12:06:56Z","issue":"2","type":"journal_article","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"citation":{"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>","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.","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>.","short":"H. Edelsbrunner, G. Stöckl, Journal of Combinatorial Theory Series A 43 (1986) 344–349.","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>","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>."},"publist_id":"2020","oa_version":"None","date_published":"1986-11-01T00:00:00Z","volume":43,"year":"1986","day":"01","status":"public","publisher":"Elsevier","publication":"Journal of Combinatorial Theory Series A","article_type":"original","date_updated":"2022-02-01T14:02:41Z","scopus_import":"1"}