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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)
Title
  • Unit Distances in Three Dimensions
  • Unit Distances in Three Dimensions (en)
skos:prefLabel
  • Unit Distances in Three Dimensions
  • Unit Distances in Three Dimensions (en)
skos:notation
  • RIV/00216208:11320/12:10126157!RIV13-MSM-11320___
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  • P(1M0545), S
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  • 4
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  • 175997
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  • RIV/00216208:11320/12:10126157
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  • unit distance (en)
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [46A0B651C09D]
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  • Combinatorics Probability and Computing
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  • 21
http://linked.open...iv/tvurceVysledku
  • Matoušek, Jiří
  • Safernová, Zuzana
  • Sharir, Micha
  • Kaplan, Haim
http://linked.open...ain/vavai/riv/wos
  • 000304915900008
issn
  • 0963-5483
number of pages
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  • 10.1017/S0963548312000144
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  • 11320
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