Cyclic flats and corners of the linking polynomial

Let T(M; x,y) = ∑_ij T_ij xⁱy^jdenote the Tutte polynomial of the matroid M. If T_ij is a corner of T (M; x, y), then T_ij counts the sets of corank i and nullity j and each such set is a cyclic flat of M. The main result of this article consists of extending the definition of cyclic flats to a pair of matroids and proving that the corners of the linking polynomial give the lower bound of the number of the cyclic flats of the matroid pair.