The cyclic flats of a q -matroid.

In this paper we develop the theory of cyclic flats of q -matroids. We show that the cyclic flats, together with their ranks, uniquely determine a q -matroid and hence derive a new q -cryptomorphism. We introduce the notion of F q m -independence of an F q -subspace of F q n and we show that q -matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.