[{"_id":"2429","status":"public","type":"journal_article","extern":1,"citation":{"mla":"Matoušek, Jiří, et al. “K-Sets in Four Dimensions.” Discrete & Computational Geometry, vol. 35, no. 2, Springer, 2006, pp. 177–91, doi:10.1007/s00454-005-1200-4.","ieee":"J. Matoušek, M. Sharir, S. Smorodinsky, and U. Wagner, “K-sets in four dimensions,” Discrete & Computational Geometry, vol. 35, no. 2. Springer, pp. 177–191, 2006.","short":"J. Matoušek, M. Sharir, S. Smorodinsky, U. Wagner, Discrete & Computational Geometry 35 (2006) 177–191.","apa":"Matoušek, J., Sharir, M., Smorodinsky, S., & Wagner, U. (2006). K-sets in four dimensions. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-005-1200-4","ama":"Matoušek J, Sharir M, Smorodinsky S, Wagner U. K-sets in four dimensions. Discrete & Computational Geometry. 2006;35(2):177-191. doi:10.1007/s00454-005-1200-4","chicago":"Matoušek, Jiří, Micha Sharir, Shakhar Smorodinsky, and Uli Wagner. “K-Sets in Four Dimensions.” Discrete & Computational Geometry. Springer, 2006. https://doi.org/10.1007/s00454-005-1200-4.","ista":"Matoušek J, Sharir M, Smorodinsky S, Wagner U. 2006. K-sets in four dimensions. Discrete & Computational Geometry. 35(2), 177–191."},"date_updated":"2021-01-12T06:57:26Z","title":"K-sets in four dimensions","author":[{"first_name":"Jiří","last_name":"Matoušek","full_name":"Matoušek, Jiří"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"full_name":"Smorodinsky, Shakhar","last_name":"Smorodinsky","first_name":"Shakhar"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568","full_name":"Uli Wagner","last_name":"Wagner"}],"publist_id":"4495","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. "}],"intvolume":" 35","month":"02","publisher":"Springer","quality_controlled":0,"publication":"Discrete & Computational Geometry","day":"01","publication_status":"published","year":"2006","date_created":"2018-12-11T11:57:37Z","issue":"2","volume":35,"date_published":"2006-02-01T00:00:00Z","doi":"10.1007/s00454-005-1200-4","page":"177 - 191"}]