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Semiovals with large collinear subsets
Authors:Jeremy M Dover
Institution:(1) 445 Poplar Leaf Dr., 21037 Edgewater, MD, USA
Abstract:Asemioval in a projective plane Pgr is a setS of points such that for every pointP epsi S, there exists a unique line ell of Pgr such thatellcapS={P}. In other words, at every point ofS, there exists a unique tangent line.In this paper, we consider semiovals such that some line has a ldquolargerdquo intersection withS. In a finite plane Pgr it is shown that no semioval can contain a full line, and that apart from two small cases, no semioval can contain all but one point of some line. We then consider semiovals which contain all but two points of some line, providing some examples and characterizations.
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