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A dual approach to embedding the complement of two lines in a finite projective plane

Part of: Finite geometry and special incidence structures Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Lynn Margaret Batten
Lynn Margaret Batten
Affiliation:
Department of Mathematics and Astronomy University of ManitobaWinnipeg, ManitobaCanadaR3T 2N2
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Abstract

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Let S be a finite linear space on v ≥ n2 –n points and b = n2+n+1–m lines, m ≧ 0, n ≧ 1, such that at most m points are not on n + 1 lines. If m ≧ 1, except if m = 1 and a unique point on n lines is on no line with two points, then S embeds uniquely in a projective plane of order n or is one exceptional case if n =4. If m ≦ 1 and if v ≧ n2 – 2√n + 3, + 6, the same conclusion holds, except possibly for the uniqueness.

1991 Mathematics subject classification (Amer. Math. Soc.) 05 B 05, 51 E 10.

MSC classification

Secondary: 05B05: Block designs 51E10: Steiner systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 3 , December 1991 , pp. 426 - 435
Copyright
Copyright © Australian Mathematical Society 1991

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