Matroids (also called combinatorial geometries) present a strong combinatorial generalization of graphs and matrices. Unlike isomorph-free generation of graphs, which has been extensively studied both from theoretical and practical points of view, not much research has been done so far about matroid generation. Perhaps the main problem with matroid generation lies in a very complex internal structure of a matroid. That is why we focus on generation of suitable matroid representations, and we

more »

... line a way how to exhaustively generate matroid representations over finite fields in reasonable computing time. In particular, we extend here some enumeration results on binary (over the binary field) combinatorial geometries by Kingan et al. We use the matroid generation algorithm of [P. Hliněný, Equivalence-Free Exhaustive Generation of Matroid Representations] and its implementation in Macek; see http://www.mcs.vuw.ac.nz/research/macek. An extended abstract prepared for AACC 2005 on August 26, 2005. . .