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The $$f$$-vector of a representable-matroid complex is log-concave. (English) Zbl 1301.05382
Summary: We show that the $$f$$-vector of the matroid complex of a representable matroid is log-concave. This proves the representable case of a conjecture made by J. H. Mason [“Matroids: unimodal conjectures and Motzkin’s theorem”, in: D. J. A. Welsh (ed.) et al., Combinatorics. Proceedings of the conference on combinatorial mathematics held at the Mathematical Institute, Oxford, 1972. Southend-on-Sea: The Institute of Mathematics and its Applications. 207–220 (1972; Zbl 0469.05001)].

##### MSC:
 05E45 Combinatorial aspects of simplicial complexes 05C31 Graph polynomials 05B35 Combinatorial aspects of matroids and geometric lattices
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##### References:
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