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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]. (en)
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Title
| - Unit Distances in Three Dimensions
- Unit Distances in Three Dimensions (en)
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skos:prefLabel
| - Unit Distances in Three Dimensions
- Unit Distances in Three Dimensions (en)
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skos:notation
| - RIV/00216208:11320/12:10126157!RIV13-MSM-11320___
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http://linked.open...avai/predkladatel
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/12:10126157
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - GB - Spojené království Velké Británie a Severního Irska
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Combinatorics Probability and Computing
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Matoušek, Jiří
- Safernová, Zuzana
- Sharir, Micha
- Kaplan, Haim
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http://linked.open...ain/vavai/riv/wos
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issn
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number of pages
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http://bibframe.org/vocab/doi
| - 10.1017/S0963548312000144
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http://localhost/t...ganizacniJednotka
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is http://linked.open...avai/riv/vysledek
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