The regular types of these structures can be represented over all fields and are precisely those that don't contain the four-point line, the Fano plane, and its dual.
If one of these structures is GF-four representable, then all GF-four representations of these objects are equivalent. R-sub-ten is a unique splitter for a certain class of these structures according to Seymour. One of these structures of rank r is uniform if and only if all of its circuits have exactly r plus one elements. The regular types of these structures can be represented over all fields and are precisely those that don't contain the four-point line, the Fano plane, and its dual. The Tutte polynomial of these structures is a generalization of the (*) characteristic polynomial to two variables. Maximal independent ones of these are bases.  These are defined on a ground set and an independent collection of subsets. These structures provide strong connections between graph theory and linear algebra. For 10 points, name these combinatorial structures that generalize the concept of linear independence to matrices.
If one of these structures is GF-four representable, then all GF-four representations of these objects are equivalent.
matroids