Generalized permutohedra, h-vectors of cotransversal matroids and pure O-sequences (extended abstract) - Archive ouverte HAL Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2011

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.
Stanley a conjecturé que le h-vecteur d'un complexe matroïde est une pure O-séquence. Nous allons le prouver pour les matroïdes cotransversaux en utilisant generalized permutohedra. Nous construisons une bijection entre les points du réseau intérieur d'un polytope convexe $r$-dimensions et les bases d'un matroïde transversal $r$-rang.
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Dates and versions

hal-01215056 , version 1 (13-10-2015)

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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, ⟨10.46298/dmtcs.2946⟩. ⟨hal-01215056⟩

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