Journal of Commutative Algebra

Sperner property and finite-dimensional Gorenstein algebras associated to matroids

Toshiaki Maeno and Yasuhide Numata

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

Article information

Source
J. Commut. Algebra, Volume 8, Number 4 (2016), 549-570.

Dates
First available in Project Euclid: 27 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jca/1477600747

Digital Object Identifier
doi:10.1216/JCA-2016-8-4-549

Mathematical Reviews number (MathSciNet)
MR3566530

Zentralblatt MATH identifier
1360.13048

Subjects
Primary: 13E10: Artinian rings and modules, finite-dimensional algebras
Secondary: 05B35: Matroids, geometric lattices [See also 52B40, 90C27] 06A11: Algebraic aspects of posets 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Keywords
Sperner property Lefschetz property matroid Gorenstein algebra

Citation

Maeno, Toshiaki; Numata, Yasuhide. Sperner property and finite-dimensional Gorenstein algebras associated to matroids. J. Commut. Algebra 8 (2016), no. 4, 549--570. doi:10.1216/JCA-2016-8-4-549. https://projecteuclid.org/euclid.jca/1477600747


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