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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10126157%21RIV13-MSM-11320___
rdf:type
n17:Vysledek skos:Concept
rdfs:seeAlso
http://dx.doi.org/10.1017/S0963548312000144
dcterms:description
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]. 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].
dcterms:title
Unit Distances in Three Dimensions Unit Distances in Three Dimensions
skos:prefLabel
Unit Distances in Three Dimensions Unit Distances in Three Dimensions
skos:notation
RIV/00216208:11320/12:10126157!RIV13-MSM-11320___
n17:predkladatel
n19:orjk%3A11320
n3:aktivita
n16:S n16:P
n3:aktivity
P(1M0545), S
n3:cisloPeriodika
4
n3:dodaniDat
n9:2013
n3:domaciTvurceVysledku
n4:3374041 n4:2414767
n3:druhVysledku
n10:J
n3:duvernostUdaju
n20:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
175997
n3:idVysledku
RIV/00216208:11320/12:10126157
n3:jazykVysledku
n8:eng
n3:klicovaSlova
unit distance
n3:klicoveSlovo
n15:unit%20distance
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[46A0B651C09D]
n3:nazevZdroje
Combinatorics Probability and Computing
n3:obor
n14:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
4
n3:projekt
n21:1M0545
n3:rokUplatneniVysledku
n9:2012
n3:svazekPeriodika
21
n3:tvurceVysledku
Safernová, Zuzana Kaplan, Haim Matoušek, Jiří Sharir, Micha
n3:wos
000304915900008
s:issn
0963-5483
s:numberOfPages
14
n13:doi
10.1017/S0963548312000144
n12:organizacniJednotka
11320