Title

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

Document Type

Article

Publication Date

12-1-1988

Abstract

Let q 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 most n2. In this paper, we show that, with the exception of n = 3, a rank-n geometry that is representable over GF(3) and GF(q) and contains exactly n2 points is isomorphic to the rank-n Dowling geometry based on the multiplicative group of GF(3). © 1988 Springer-Verlag.

Publication Source (Journal or Book title)

Graphs and Combinatorics

First Page

323

Last Page

332

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