Geodesic
On the Sperner property and Gorenstein Algebras Associated to Matroids
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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We introduce a certain class of algebras associated to matroids. We prove the Lefschetz property of the algebras for some special cases. Our result implies the Sperner property for the Boolean lattice and the vector space lattice. 
@article{DMTCS_2012_special_263_a14,
     author = {Maeno, Toshiaki and Numata, Yasuhide},
     title = {On the {Sperner} property and {Gorenstein} {Algebras} {Associated} to {Matroids}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3028/}
}
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Maeno, Toshiaki; Numata, Yasuhide. On the Sperner property and Gorenstein Algebras Associated to Matroids. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3028. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3028/

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