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