Abstract
According to the definition of the famous Italian geometer, Beniamino Segre, an oval of a finite projective plane is a maximal sized set of points, no three of which are collinear. One of the most influential theorems of finite geometry has been Segre's 1954 result that every oval of a finite Desarguesian plane of odd order is an irreducible conic. In 1957 and 1962 he showed that the even order case is more complicated by constructing two infinite sequences of nonconic ovals in Desarguesian planes of even order. This paper doubles the number of known sequences of ovals in these planes from two to four. Also a short survey of results about ovals is given.
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© 1983 Springer-Verlag
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Glynn, D.G. (1983). Two new sequences of ovals in finite desarguesian planes of even order. In: Casse, L.R.A. (eds) Combinatorial Mathematics X. Lecture Notes in Mathematics, vol 1036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071521
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DOI: https://doi.org/10.1007/BFb0071521
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