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Generalized permutohedra, h-vectors of cotransversal matroids and pure O-sequences (extended abstract)

Abstract : Stanley has conjectured that the h-vector of a matroid complex is a pure O-sequence. We will prove this for cotransversal matroids by using generalized permutohedra. We construct a bijection between lattice points inside a $r$-dimensional convex polytope and bases of a rank $r$ transversal matroid.
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Suho Oh. Generalized permutohedra, h-vectors of cotransversal matroids and pure O-sequences (extended abstract). 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.705-716. ⟨hal-01215056⟩

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