Sets of rich lines in general position

@article{Amirkhanyan2017SetsOR,
  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.},
  year={2017},
  volume={96},
  pages={67-85}
}
  • 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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    References

    SHOWING 1-10 OF 16 REFERENCES
    h-Fold Sums from a Set with Few Products
    • 24
    • PDF
    Extremal problems in discrete geometry
    • 512
    • PDF
    Extensions of a result of Elekes and Rónyai
    • 18
    • PDF
    On Rich Lines in Grids
    • 5
    • PDF
    How to find groups? (and how to use them in Erdős geometry?)
    • 52
    Perfect Matchings in ε-Regular Graphs and the Blow-Up Lemma
    • 57
    On the number of sums and products
    • 135
    • PDF
    On sum sets of sets having small product set
    • 54
    • PDF
    On a Certain Generalization of the Balog-Szemerédi-Gowers Theorem
    • 8
    • PDF
    Additive combinatorics
    • T. Tao, V. Vu
    • Computer Science
    • Cambridge studies in advanced mathematics
    • 2007
    • 764
    • PDF