On sign-representable matroids

A matroid M will be called sign-representable if, for every basis B of M, there is a (0,1, — 1)-matrix [Ir Ι Y] representing M over Q in which the first r columns correspond to the members of B. The class of sign-representable matroids, which is closely related to the important class of regular matroids, is easily seen to be closed under both duality and the taking of minors. This paper proves several characterizations of the class, including a constructive one, and shows that the excluded minors for the class are U2,5, U 3,5, the Fano matroid and its dual, and the rank-3 whirl. © 1993, Cambridge Philosophical Society. All rights reserved