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arXiv · 2102.11790

Renitent lines

Bence Csajbók·Peter Sziklai·Zsuzsa Weiner
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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 $p$, the characteristic). The lines with exceptional intersection numbers are called renitent, and we prove results on the (regular) behaviour of these renitent lines.

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Bence Csajbók, Peter Sziklai, Zsuzsa Weiner. 2023-09-08. Renitent lines. https://doi.org/10.1016/j.ejc.2023.103792

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