Renitent lines
Abstract
There are many examples for point sets in finite geometry, which behave "almost regularly" in some (well-defined) sense, for instance they have "almost 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 , the characteristic). The lines with exceptional intersection numbers are called renitent, and we prove results on the (regular) behaviour of these renitent lines.
Keywords
Cite
@article{arxiv.2102.11790,
title = {Renitent lines},
author = {Bence Csajbók and Peter Sziklai and Zsuzsa Weiner},
journal= {arXiv preprint arXiv:2102.11790},
year = {2023}
}
Comments
The sharpness of some statements has been proved. There are some new examples and a new section about some dual statements and their consequences regarding the geometric properties of codewords of the $\mathbb{F}_p$-linear code generated by characteristic vectors of lines of $\mathrm{PG}(2,q)$. The latter result generalise an old result of Blokhuis, Brouwer and Wilbrink