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On the \(h\)-vector of a lattice path matroid. (English) Zbl 1267.05057

Summary: Stanley has conjectured that the \(h\)-vector of a matroid complex is a pure \(M\)-vector. We prove a strengthening of this conjecture for lattice path matroids by constructing a corresponding family of discrete polymatroids.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
05E45 Combinatorial aspects of simplicial complexes
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