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)

Authors: Suho Oh 1

  • 1 Department of Mathematics [MIT]

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.

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: pure O-sequence,polytope,matching,generalized permutohedra,Stanley's conjecture,h-vector,matroid,cotransversal,bipartite,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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