The Cyclic Flats of a q-Matroid
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In this paper we develop the theory of cyclic flats of q-matroids. We show that the lattice of cyclic flats, together with their ranks, uniquely determines 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.
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