Discrete & Computational Geometry

, Volume 5, Issue 1, pp 83–95 | Cite as

Combinatorial geometries representable over GF(3) and GF(q). I. The number of points

  • Joseph P. S. Kung
Article

Abstract

Letq be a prime power not divisible by 3. We show that the number of points (or rank-1 flats) in a combinatorial geometry (or simple matroid) of rankn representable over GF(3) and GF(q) is at mostn2. Whenq is odd, this bound is sharp and is attained by the Dowling geometries over the cyclic group of order 2.

Keywords

Discrete Comput Geom Prime Power Rank Function Line Incident Minimum Rank 

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Joseph P. S. Kung
    • 1
  1. 1.Department of MathematicsNorth Texas State UniversityDentonUSA

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