Sets of rich lines in general position

  title={Sets of rich lines in general position},
  author={G. Amirkhanyan and A. Bush and E. Croot and Chris Pryby},
  journal={J. Lond. Math. Soc.},
  • G. Amirkhanyan, A. Bush, +1 author Chris Pryby
  • Published 2017
  • Mathematics, Computer Science
  • J. Lond. Math. Soc.
  • Given a set of $n$ points in $R^2$, the Szemeredi-Trotter theorem establishes that the number of lines which can be incident to at least $k > 1$ of these points is $O(n^2/k^3 + n/k)$. J.\ Solymosi conjectured that if one requires the points to be in a grid formation and the lines to be in general position---no two parallel, no three meeting at a point---then one can get a much tighter bound. We prove: for every $\epsilon > 0$ there exists some $\delta > 0$ such that for sufficiently large… CONTINUE READING
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