Realization of Rank 3 Matroids

by Franz B. Kalhoff

Abstract:
By mainly algebraic means, in a paper to appear in Discrete Math. we have shown that each finite linear space embeds into the projective plane over some (not necessarily associative) division algebra. Here we shall give a matroid theoretic interpretation of this result. In particular, we present the prototypes for coordinatizing arbitrary rank three matroids: a kind of three dimensional vector spaces over division algebras.

Key words and phrases: Coordinatization, Division Algebra, Matroid, Rank three Matroid

1991 Mathematics Subject Classification: Primary 05 B 35; Secondary 17 A 35.

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Contact: Franz.Kalhoff@Mathematik.Uni-Dortmund.DE