Blocking semiovals containing conics
-
J. M. Dover
,
K. E. Mellinger
and
K. L. Wantz
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.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- Masthead
- A class of lattices and boolean functions related to the Manickam–Miklös–Singhi conjecture
- Blocking semiovals containing conics
- On universal covers in normed planes
- Stability results for some classical convexity operations
- Pseudo-embeddings and pseudo-hyperplanes
- Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
- Metrics in the family of star bodies
- Ellipsoid characterization theorems
- Logarithmic limit sets of real semi-algebraic sets
Articles in the same Issue
- Masthead
- A class of lattices and boolean functions related to the Manickam–Miklös–Singhi conjecture
- Blocking semiovals containing conics
- On universal covers in normed planes
- Stability results for some classical convexity operations
- Pseudo-embeddings and pseudo-hyperplanes
- Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
- Metrics in the family of star bodies
- Ellipsoid characterization theorems
- Logarithmic limit sets of real semi-algebraic sets
