On the Sperner property and Gorenstein Algebras Associated to Matroids

Abstract

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.

Keywords

• lefschetz property
• ranked poset
• universal grôbner bases.
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]