Journal of Geometry

, Volume 107, Issue 1, pp 119–123 | Cite as

A minimum blocking semioval in PG(2, 9)

  • Jeremy M. Dover
  • Keith E. Mellinger
  • Kenneth L. Wantz
Article
  • 61 Downloads

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). The minimum size of a blocking semioval is currently known in all projective planes of order < 11, with the exception of PG(2, 9). In this note we show by demonstration of an example that the smallest blocking semioval in PG(2, 9) has size 21 and investigate some properties of this set.

Mathematics Subject Classification

51E20 

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Copyright information

© Springer Basel AG 2015

Authors and Affiliations

  • Jeremy M. Dover
    • 1
  • Keith E. Mellinger
    • 2
  • Kenneth L. Wantz
    • 3
  1. 1.Dover Networks LLCEdgewaterUSA
  2. 2.Department of MathematicsUniversity of Mary WashingtonFredericksburgUSA
  3. 3.Department of MathematicsRegent UniversityVirginia BeachUSA

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