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Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries

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Abstract

Letq be an odd prime power not divisible by 3. In Part I of this series, it was shown that the number of points in a rank-n combinatorial geometry (or simple matroid) representable over GF(3) and GF(q) is at mostn 2. In this paper, we show that, with the exception ofn = 3, a rank-n geometry that is representable over GF(3) and GF(q) and contains exactlyn 2 points is isomorphic to the rank-n Dowling geometry based on the multiplicative group of GF(3).

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Authors and Affiliations

  1. Department of Mathematics, North Texas State University, 76203, Denton, TX, USA

    Joseph P. S. Kung

  2. Department of Mathematics, Louisiana State University, 70803, Baton Rouge, LA, USA

    James G. Oxley

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  1. Joseph P. S. Kung
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  2. James G. Oxley
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This research was partially supported by the National Science Foundation under Grants DMS-8521826 and DMS-8500494.

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Kung, J.P.S., Oxley, J.G. Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries. Graphs and Combinatorics 4, 323–332 (1988). https://doi.org/10.1007/BF01864171

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  • DOI: https://doi.org/10.1007/BF01864171

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