IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-85729-106-6_7.html
   My bibliography  Save this book chapter

Resolutions of monomial ideals and the Eliahou–Kervaire formula

In: Monomial Ideals

Author

Listed:
  • Jürgen Herzog

    (Universität Duisburg-Essen, Fachbereich Mathematik)

  • Takayuki Hibi

    (Osaka University, Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology)

Abstract

Chapter 7 discusses minimal free resolutions of monomial ideals. We derive formulas for the graded Betti numbers of stable and squarefree stable ideals, and use these formulas to deduce the Bigatti–Hulett theorem which says that lexsegment ideals have the largest graded Betti numbers among all graded ideals with the same Hilbert function. We also present the squarefree analogue of the Bigatti–Hulett theorem, and give the comparison of Betti numbers over the symmetric and exterior algebra.

Suggested Citation

  • Jürgen Herzog & Takayuki Hibi, 2011. "Resolutions of monomial ideals and the Eliahou–Kervaire formula," Springer Books, in: Monomial Ideals, chapter 7, pages 115-128, Springer.
    • Handle: RePEc:spr:sprchp:978-0-85729-106-6_7
    DOI: 10.1007/978-0-85729-106-6_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-0-85729-106-6_7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.