On a question of bourgain about geometric incidences

  • Authors:
  • JÓzsef Solymosi;Csaba d. TÓth

  • Affiliations:
  • Department of mathematics, university of british columbia, 1984 mathematics road, vancouver, bc, canadav6t 1z2 (e-mail: solymosi@math.ubc.ca);Department of mathematics, university of calgary, 2500 university drive nw, calgary, ab, canadat2n 1n4 (e-mail: cdtoth@ucalgary.ca)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2008

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Abstract

Given a set of s points and a set of n2 lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, we show that s = Ω(n11/4). This is the first non-trivial answer to a question recently posed by Jean Bourgain.