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