Sperner property and finite-dimensional Gorenstein algebras associated to matroids
arXiv:1107.5094
Abstract
We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras associated to matroids. Our result implies the Sperner property of the vector space lattice. More generally, it is shown that the modular geometric lattice has the Sperner property. We also discuss the Gröbner fan of the defining ideal of our Gorenstein algebra.
New section on modular geometric lattices