IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2024i1p34-d1553772.html
   My bibliography  Save this article

Complete Homogeneous Symmetric Polynomials with Repeating Variables

Author

Listed:
  • Luis Angel González-Serrano

    (Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Mexico City 07738, Mexico)

  • Egor A. Maximenko

    (Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Mexico City 07738, Mexico)

Abstract

In this paper, we consider complete homogeneous symmetric polynomials evaluated for variables repeated with given multiplicities; in other words, we consider polynomials obtained from complete homogeneous polynomials by identifying some subsets of their variables. We represent such polynomials as linear combinations of the powers of the variables, where all exponents are equal to the degree of the original polynomial. We give two proofs for the proposed formulas: the first proof uses the decomposition of the generating function into partial fractions, and the second involves the inverse of the confluent Vandermonde matrix. We also discuss the computational feasibility of the proposed formulas.

Suggested Citation

  • Luis Angel González-Serrano & Egor A. Maximenko, 2024. "Complete Homogeneous Symmetric Polynomials with Repeating Variables," Mathematics, MDPI, vol. 13(1), pages 1-27, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:34-:d:1553772
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/1/34/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/1/34/
    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:13:y:2024:i:1:p:34-:d:1553772. 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.