Innovations in Incidence Geometry
- Innov. Incidence Geom.
- Volume 14, Number 1 (2015), 1-26.
Semiarcs with a long secant in PG(2,q)
A -semiarc is a point set with the property that the number of tangent lines to at each of its points is . We show that if a small -semiarc in has a large collinear subset , then the tangents to at the points of can be blocked by points not in . In fact, we give a more general result for small point sets with less uniform tangent distribution. We show that in small -semiarcs are related to certain small blocking sets and give some characterization theorems for small semiarcs with large collinear subsets.
Innov. Incidence Geom., Volume 14, Number 1 (2015), 1-26.
Received: 19 July 2013
Accepted: 6 October 2014
First available in Project Euclid: 28 February 2019
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Csajbók, Bence; Héger, Tamás; Kiss, György. Semiarcs with a long secant in PG(2,q). Innov. Incidence Geom. 14 (2015), no. 1, 1--26. doi:10.2140/iig.2015.14.1. https://projecteuclid.org/euclid.iig/1551323025