On regular semiovals in PG(2,q)
András Gács
Eötvös Loránd University Department of Computer Science Pázmány Péter sétány 1/C H-1117 Budapest Hungary Pázmány Péter sétány 1/C H-1117 Budapest Hungary
DOI: 10.1007/s10801-006-6029-2
Abstract
In this paper we prove that a point set in PG(2, q) meeting every line in 0, 1 or r points and having a unique tangent at each of its points is either an oval or a unital. This answers a question of Blokhuis and Szönyi [1].
Pages: 71–77
Keywords: keywords semioval; oval; unital; polynomials
Full Text: PDF
References
1. A. Blokhuis and T. Sz\Acute\Acute onyi, “Note on the structure of semiovals in finite projective planes,” Discrete Mathematics 106/107 (1992), 61-65.
2. J.W.P. Hirschfeld, Projective geometries over finite fields, 2nd edn., Clarendon Press, Oxford, 1979, 1998.
3. Gy. Kiss and J. Ruff, “Note on small semiovals,” Annales Univ. Sci. Budapest 47 (2004), 143-151.
4. Gy. Kiss, Small semiovals in P G(2, q), J. of Geometry, submitted.
5. J.A. Thas, “A combinatorial characterization of Hermitan curves,” Journal of Algebraic Combinatorics 1 (1992), 97-102.
6. A. Blokhuis, Gy. Kiss, I. Kovács, A. Malni\check c, D. Maru\check si\check c, and J. Ruff, Semiovals contained in the union of three concurrent lines, J. Comb. Designs, submitted.
2. J.W.P. Hirschfeld, Projective geometries over finite fields, 2nd edn., Clarendon Press, Oxford, 1979, 1998.
3. Gy. Kiss and J. Ruff, “Note on small semiovals,” Annales Univ. Sci. Budapest 47 (2004), 143-151.
4. Gy. Kiss, Small semiovals in P G(2, q), J. of Geometry, submitted.
5. J.A. Thas, “A combinatorial characterization of Hermitan curves,” Journal of Algebraic Combinatorics 1 (1992), 97-102.
6. A. Blokhuis, Gy. Kiss, I. Kovács, A. Malni\check c, D. Maru\check si\check c, and J. Ruff, Semiovals contained in the union of three concurrent lines, J. Comb. Designs, submitted.