On the Sperner property and Gorenstein Algebras Associated to Matroids

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. Nous présentons une classe d'algèbres associées aux matroïdes. N...

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Vydáno v:Discrete Mathematics & Theoretical Computer Science Ročník DMTCS Proceedings vol. AR,...; číslo Proceedings; s. 157 - 168
Hlavní autoři: Maeno, Toshiaki, Numata, Yasuhide
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
japonština
Vydáno: Centre pour la Communication Scientifique Directe (CCSD) 01.01.2012
DMTCS
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Edice:DMTCS Proceedings
Témata:
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Computer Science
Discrete Mathematics
lefschetz property
Mathematics
QA1-939
ranked poset
universal Grôbner bases
Lefschetz property
ranked poset
universal Grôbner bases
ISSN:1365-8050, 1462-7264, 1365-8050
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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. Nous présentons une classe d'algèbres associées aux matroïdes. Nous démontrons que dans quelques cas spécifiques, ces algèbres vérifient la propriété de Lefschetz. Notre résultat implique la propriété de Sperner pour l'algèbre de Boole et pour le poset d'espace vectoriel.
AbstractList 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. Nous présentons une classe d'algèbres associées aux matroïdes. Nous démontrons que dans quelques cas spécifiques, ces algèbres vérifient la propriété de Lefschetz. Notre résultat implique la propriété de Sperner pour l'algèbre de Boole et pour le poset d'espace vectoriel.
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.
Author Maeno, Toshiaki
Numata, Yasuhide
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Contributor Department of Electrical Engineering [Kyoto] ; Kyoto University
Hiro-Fumi Yamada and Nantel Bergeron
Department of Mathematical Informatics (University of Tokyo) ; The University of Tokyo (UTokyo)
Department of Electrical Engineering [Kyoto] ; Kyoto University [Kyoto]
Japan Science and Technology Agency (JST)
Episciences Iam, Coordination
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ranked poset
universal Grôbner bases
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Snippet 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...
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SubjectTerms [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Computer Science
Discrete Mathematics
lefschetz property
Mathematics
QA1-939
ranked poset
universal Grôbner bases
Title On the Sperner property and Gorenstein Algebras Associated to Matroids
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