. "[46A0B651C09D]" . "Safernov\u00E1, Zuzana" . "Unit Distances in Three Dimensions"@en . "Unit Distances in Three Dimensions"@en . "Unit Distances in Three Dimensions" . "http://dx.doi.org/10.1017/S0963548312000144" . "Kaplan, Haim" . . . "RIV/00216208:11320/12:10126157" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "Matou\u0161ek, Ji\u0159\u00ED" . . "0963-5483" . "11320" . "Unit Distances in Three Dimensions" . "10.1017/S0963548312000144" . . . . . "Combinatorics Probability and Computing" . "4"^^ . . "Sharir, Micha" . . "We show that the number of unit distances determined by n points in R-3 is O(n(3/2)), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28]."@en . . "4" . "000304915900008" . . "14"^^ . "21" . . "We show that the number of unit distances determined by n points in R-3 is O(n(3/2)), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28]." . "P(1M0545), S" . . "2"^^ . . "RIV/00216208:11320/12:10126157!RIV13-MSM-11320___" . "175997" . "unit distance"@en . .