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

dmtcs:2946 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2946
Generalized permutohedra, h-vectors of cotransversal matroids and pure O-sequences (extended abstract)Conference paper

Authors: Suho Oh 1

  • 1 Department of Mathematics [MIT]

[en]
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.

[fr]
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.

https://doi.org/10.46298/dmtcs.2946
Source: HAL:hal-01215056v1
Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] generalized permutohedra, Stanley's conjecture, h-vector, matroid, cotransversal, bipartite, matching, polytope, pure O-sequence

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