On the Sperner property and Gorenstein Algebras Associated to Matroids
نویسندگان
چکیده
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. Résumé. Nous présentons une classe d’algèbres associées aux matroı̈des. Nous démontrons que dans quelques cas spécifiques, ces algèbres verifient la propriété de Lefschetz. Notre résultat implique la propriété de Sperner pour l’algèbre de Boole et pour le poset d’espace vectoriel.
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