Sperner property and finite-dimensional Gorenstein algebras associated to matroids

2011/07/25 by Toshiaki Maeno, Maeno, Toshiaki, Yasuhide Numata +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1107.5094

New section on modular geometric lattices

arxiv created 2011/11/21 · arxiv updated 2011/11/22

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.

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