{"title":"K-sets in four dimensions","extern":1,"publication_status":"published","status":"public","month":"02","type":"journal_article","year":"2006","volume":35,"publisher":"Springer","day":"01","date_created":"2018-12-11T11:57:37Z","date_published":"2006-02-01T00:00:00Z","quality_controlled":0,"date_updated":"2021-01-12T06:57:26Z","_id":"2429","abstract":[{"text":"We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane. ","lang":"eng"}],"publication":"Discrete & Computational Geometry","publist_id":"4495","author":[{"last_name":"Matoušek","full_name":"Matoušek, Jiří","first_name":"Jiří"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"first_name":"Shakhar","full_name":"Smorodinsky, Shakhar","last_name":"Smorodinsky"},{"full_name":"Uli Wagner","last_name":"Wagner","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"}],"citation":{"short":"J. Matoušek, M. Sharir, S. Smorodinsky, U. Wagner, Discrete &#38; Computational Geometry 35 (2006) 177–191.","ama":"Matoušek J, Sharir M, Smorodinsky S, Wagner U. K-sets in four dimensions. <i>Discrete &#38; Computational Geometry</i>. 2006;35(2):177-191. doi:<a href=\"https://doi.org/10.1007/s00454-005-1200-4\">10.1007/s00454-005-1200-4</a>","ista":"Matoušek J, Sharir M, Smorodinsky S, Wagner U. 2006. K-sets in four dimensions. Discrete &#38; Computational Geometry. 35(2), 177–191.","ieee":"J. Matoušek, M. Sharir, S. Smorodinsky, and U. Wagner, “K-sets in four dimensions,” <i>Discrete &#38; Computational Geometry</i>, vol. 35, no. 2. Springer, pp. 177–191, 2006.","mla":"Matoušek, Jiří, et al. “K-Sets in Four Dimensions.” <i>Discrete &#38; Computational Geometry</i>, vol. 35, no. 2, Springer, 2006, pp. 177–91, doi:<a href=\"https://doi.org/10.1007/s00454-005-1200-4\">10.1007/s00454-005-1200-4</a>.","apa":"Matoušek, J., Sharir, M., Smorodinsky, S., &#38; Wagner, U. (2006). K-sets in four dimensions. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-005-1200-4\">https://doi.org/10.1007/s00454-005-1200-4</a>","chicago":"Matoušek, Jiří, Micha Sharir, Shakhar Smorodinsky, and Uli Wagner. “K-Sets in Four Dimensions.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2006. <a href=\"https://doi.org/10.1007/s00454-005-1200-4\">https://doi.org/10.1007/s00454-005-1200-4</a>."},"intvolume":"        35","issue":"2","doi":"10.1007/s00454-005-1200-4","page":"177 - 191"}