Skip to main contentSkip to search
Episciences
Open Access Journals
Sign in(new window)
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Sign in(new window)
Articles & Issues
All articlesAll accepted articlesAll volumesLast volumeSectionsSpecial issuesAuthors
About
The journalIndexing
Boards
Publish
For authorsEthical charter
Submit
Discrete Mathematics & Theoretical Computer Science logo
Contact
|
Credits
eISSN 1365-8050
|
RSS
|
Atom
Episciences
Documentation
|
Acknowledgements
|
Publishing policy
Accessibility: non-compliant
|
Legal mentions
|
Privacy statement
|
Terms of use
  1. Home > Articles & Issues >
  2. Articles >
  3. On the Sperner prope ...
Conference paper

On the Sperner property and Gorenstein Algebras Associated to Matroids

Toshiaki Maeno (1), Yasuhide Numata (2) (3)
(1) Department of Electrical Engineering [Kyoto]
(2) Department of Mathematical Informatics
(3) Japan Science and Technology Agency
Download article
Open on HAL
Imported on
January 31, 2017
Published on
December 31, 2011
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Proceedings
DOI
10.46298/dmtcs.3028
License
https://about.hal.science/hal-authorisation-v1
Indicators
513
Views
935
Downloads

On the Sperner property and Gorenstein Algebras Associated to Matroids

Toshiaki Maeno (1), Yasuhide Numata (2) (3)
(1) Department of Electrical Engineering [Kyoto]
(2) Department of Mathematical Informatics
(3) Japan Science and Technology Agency
Abstract
English
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.
French
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Lefschetz property
  • ranked poset
  • universal Grôbner bases.
Cited by

Source: OpenCitations

  • k-Lefschetz Properties

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 171-188

    DOI : 10.1007/978-3-642-38206-2_6

  • The Strong Lefschetz Property and the Schur–Weyl Duality

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 211-234

    DOI : 10.1007/978-3-642-38206-2_9

  • Cohomology Rings and the Strong Lefschetz Property

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 189-199

    DOI : 10.1007/978-3-642-38206-2_7

  • Poset Theory

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 1-38

    DOI : 10.1007/978-3-642-38206-2_1

  • Basics on the Theory of Local Rings

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 39-95

    DOI : 10.1007/978-3-642-38206-2_2

  • The eigenvalues of the Hessian matrices of the generating functions for trees with k components

    SOAR (Shinshu University)

    Authors : Akiko Yazawa ORCID

    Journal reference : Volume 631, 2021, pp. 48-66

    DOI : 10.1016/j.laa.2021.08.017

  • Complete Intersections with the SLP

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 141-156

    DOI : 10.1007/978-3-642-38206-2_4

  • Invariant Theory and Lefschetz Properties

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 201-209

    DOI : 10.1007/978-3-642-38206-2_8

  • A Generalization of Lefschetz Elements

    Lecture notes in mathematics

    Authors : Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata ORCID, Akihito Wachi, Junzo Watanabe ORCID

    Journal reference : Volume , 2013, pp. 157-170

    DOI : 10.1007/978-3-642-38206-2_5
Preview
Loading PDF preview...