# Preprints

(See also my published papers.)

Citation counts are taken from Google Scholar, which on occasion overcounts slightly.

- Dániel T. Nagy, Zoltán Lóránt Nagy, and Russ Woodroofe,
The extensible No-Three-In-Line problem.
The classical No-Three-In-Line problem seeks the maximum number of points that may be selected from an

*n*×*n*grid while avoiding a collinear triple. The maximum is well known to be linear in*n*. Following a question of Erde, we seek to select sets of large density from the infinite grid ℤ^{2}while avoiding a collinear triple. We show the existence of such a set which contains Θ(*n*/log^{1+ε}*n*) points in [1,*n*]^{2}for all*n*, where*ε*> 0 is an arbitrarily small real number. We also give computational evidence suggesting that a construction with Θ(*n*) points may exist.