Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter January 8, 2013

Blocking semiovals containing conics

J. M. Dover, K. E. Mellinger and K. L. Wantz
From the journal

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.


Research supported by a sabbatical leave from the University of Mary Washington

Published Online: 2013-01-08
Published in Print: 2013-01

© 2013 by Walter de Gruyter GmbH & Co.