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 ℤ2 while avoiding a collinear triple. We show the existence of such a set which contains Θ(n/log1+εn) 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.