Sperner property and finite-dimensional Gorenstein algebras associated to matroids

Details Sperner property and finite-dimensional Gorenstein algebras associated to matroids Sperner property and finite-dimensional Gorenstein algebras associated to matroids

2011-07-25

arxiv.org/abs/1107.5094v2

Mathematics

Commutative Algebra

New section on modular geometric lattices

Scientific paper

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
Gr\"obner fan of the defining ideal of our Gorenstein algebra.

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