Suho Oh
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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)
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https://doi.org/10.46298/dmtcs.2946
Generalized permutohedra, h-vectors of cotransversal matroids and pure O-sequences (extended abstract)
Authors: Suho Oh 1
NULL
Suho Oh
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.
Merino, Criel; Noble, Steven D.; Ramírez-Ibáñez, Marcelino; Villarroel-Flores, Rafael, 2012, On The Structure Of The H-Vector Of A Paving Matroid, European Journal Of Combinatorics, 33, 8, pp. 1787-1799, 10.1016/j.ejc.2012.04.002.