On Reid's Characterization of the Ternary Matroids.

摘要

In this paper the author proves a stronger version of a result of Ralph Reid characterizing the ternary matroids (i.e., the matroids representable over the field of 3 elements, GF(3)). In particular it is proven that a matroid is ternary if it has no series-minor of type (L sub n) for n = or > (n cells and n circuits, each of size n-1), and no series-minor of type (L* sub 5) (dual of (L sub 5), BII (Fano matroid) or BI (dual of type BII).