@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}
}

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