{"status":"public","extern":1,"page":"177 - 191","abstract":[{"lang":"eng","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. "}],"year":"2006","intvolume":"        35","issue":"2","publist_id":"4495","quality_controlled":0,"publisher":"Springer","author":[{"last_name":"Matoušek","full_name":"Matoušek, Jiří","first_name":"Jiří"},{"first_name":"Micha","last_name":"Sharir","full_name":"Sharir, Micha"},{"first_name":"Shakhar","last_name":"Smorodinsky","full_name":"Smorodinsky, Shakhar"},{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Uli Wagner","last_name":"Wagner","first_name":"Uli"}],"date_updated":"2021-01-12T06:57:26Z","month":"02","doi":"10.1007/s00454-005-1200-4","title":"K-sets in four dimensions","_id":"2429","volume":35,"citation":{"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>.","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.","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>","short":"J. Matoušek, M. Sharir, S. Smorodinsky, U. Wagner, Discrete &#38; Computational Geometry 35 (2006) 177–191.","ista":"Matoušek J, Sharir M, Smorodinsky S, Wagner U. 2006. K-sets in four dimensions. Discrete &#38; Computational Geometry. 35(2), 177–191.","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>."},"type":"journal_article","date_published":"2006-02-01T00:00:00Z","publication_status":"published","date_created":"2018-12-11T11:57:37Z","day":"01","publication":"Discrete & Computational Geometry"}