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.
Available as
- Now published as Realization of rank three matroids in Appl. Math. Letters 9 (1996), 55 - 58.
Contact: Franz.Kalhoff@Mathematik.Uni-Dortmund.DE