IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3204-d700159.html
   My bibliography  Save this article

Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves

Author

Listed:
  • Manuel B. Branco

    (Departamento de Matemáticas, Universidade de Évora, 7000-671 Evora, Portugal)

  • Isabel Colaço

    (Departamento de Matemática e Ciências Físicas, Instituto Politécnico de Beja, 7800-295 Beja, Portugal)

  • Ignacio Ojeda

    (Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain)

Abstract

Let a , b and n > 1 be three positive integers such that a and ∑ j = 0 n − 1 b j are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid of N generated by { ∑ j = 0 n − 1 b j } ∪ { ∑ j = 0 n − 1 b j + a ∑ j = 0 i − 2 b j ∣ i = 2 , … , n } is determinantal. Moreover, we prove that for n > 3 , the ideal I has a unique minimal system of generators if and only if a < b − 1 .

Suggested Citation

  • Manuel B. Branco & Isabel Colaço & Ignacio Ojeda, 2021. "Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves," Mathematics, MDPI, vol. 9(24), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3204-:d:700159
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3204/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3204/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:9:y:2021:i:24:p:3204-:d:700159. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.