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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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