Toshiaki Maeno ; Yasuhide Numata - On the Sperner property and Gorenstein Algebras Associated to Matroids

dmtcs:3028 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3028
On the Sperner property and Gorenstein Algebras Associated to MatroidsConference paper

Authors: Toshiaki Maeno 1; Yasuhide Numata 2,3

  • 1 Department of Electrical Engineering [Kyoto]
  • 2 Department of Mathematical Informatics
  • 3 Japan Science and Technology Agency

[en]
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.

[fr]
Nous présentons une classe d'algèbres associées aux matroïdes. Nous démontrons que dans quelques cas spécifiques, ces algèbres vérifient la propriété de Lefschetz. Notre résultat implique la propriété de Sperner pour l'algèbre de Boole et pour le poset d'espace vectoriel.

https://doi.org/10.46298/dmtcs.3028
Source: HAL:hal-01283139v1
Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] Lefschetz property, ranked poset, universal Grôbner bases.

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