Equivalence-free exhaustive generation of matroid representations

In this paper we present an algorithm for the problem of exhaustive equivalence-free generation of 3-connected matroids which are represented by a matrix over some finite (partial) field, and which contain a given minor. The nature of this problem is exponential. and it appears to be much harder than, say, isomorph-free generation of graphs. Still, our algorithm is very suitable for practical use. and it has been successfully implemented in our matroid computing package MACEK [http: //www.mcs.vuw.ac.nz/research/ macek, 2001-05]. (c) 2005 Elsevier B.V. All rights reserved.