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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 13, Issue 1 (Jan 2013)

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Blocking semiovals containing conics

J. M. Dover / K. E. Mellinger
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  • Department of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, Fredericksburg, VA 22401-5300, USA
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/ K. L. Wantz
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  • Department of Mathematics, Regent University, 1000 Regent University Dr., Virginia Beach, VA 23464, USA
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Published Online: 2013-01-08 | DOI: https://doi.org/10.1515/advgeom-2012-0025

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.

About the article

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


Published Online: 2013-01-08

Published in Print: 2013-01-01


Citation Information: , ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2012-0025.

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