Blocking semiovals containing conics

J. M. Dover 1 , K. E. Mellinger 2  und K. L. Wantz 3
  • 1 Dover Networks LLC, 445 Poplar Leaf Dr., Edgewater, MD 21037, USA
  • 2 Department of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, Fredericksburg, VA 22401-5300, USA
  • 3 Department of Mathematics, Regent University, 1000 Regent University Dr., Virginia Beach, VA 23464, USA

Abstract

A blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there is a unique tangent line at each point). Sz˝onyi investigated an infinite family of blocking semiovals that are formed from the union of conics contained in a particular type of algebraic pencil. In this paper, the authors look at the general problem of blocking semiovals containing conics, proving a lower bound on the size of such sets and providing several new constructions of blocking semiovals containing conics. In addition, the authors investigate the natural generalization of Sz˝onyi’s construction to other conic pencils.

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Advances in Geometry is a mathematical journal which publishes original research articles of excellent quality in the area of geometry. Geometry is a field of long-standing tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity, and geometric ideas and the geometric language permeate all of mathematics.

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