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

  title={Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries},
  author={Joseph P. S. Kung and James G. Oxley},
  journal={Graphs and Combinatorics},
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 n z. 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 n z points is isomorphic to the rank-n Dowling geometry based on the multiplicative group of GF(3). 

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Showing 1-9 of 9 references

ed.): Theory of matroids

N. L. White
View 1 Excerpt

Signed graphs

Discrete Applied Mathematics • 1982
View 1 Excerpt

Decomposition of regular matroids

J. Comb. Theory, Ser. B • 1980
View 1 Excerpt

Matroid representation over GF(3)

J. Comb. Theory, Ser. B • 1979
View 1 Excerpt

A class ofgeometric lattices based on finite groups

T. A. Dowling
J. Comb. Theory (B) 14, 6186 • 1973
View 2 Excerpts

A q-analog of the partition lattice. In: A Survey of Combinatorial Theory (J.N

T. A. Dowling
View 1 Excerpt

On linear systems with integral valued solutions

I. Heller
Pacific J. Math. 7, 1351-1354 • 1957

A qanalog of the partition lattice

T. A. Dowling

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