Renitent lines.
Bence Csajbók, Péter Sziklai, Zsuzsa Weiner · arXiv (Cornell University) · 2021
There are many examples for point sets in finite geometry, which behave regularly in some (well-defined) sense, for instance they have regular line-intersection numbers. In this paper we investigate point sets of a desarguesian affine plane, for which there exist some (sometimes: many) parallel classes of lines, such that almost all lines of one parallel class intersect our set in the same number of points (possibly mod $p$, the characteristic). The lines with exceptional intersection numbers are called renitent, and we prove results on the (regular) behaviour of these renitent lines.