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 [I(r)\Y] representing M over Q in whi ch the first r columns correspond to the members of B. The class of si gn-representable matroids, which is closely related to the important c lass of regular matroids, is easily seen to be closed under both duali ty and the taking of minors. This paper proves several characterizatio ns of the class, including a constructive one, and shows that the excl uded minors for the class are U2,5, U3,5, the Fano matroid and its dua l, and the rank-3 whirl.