The Waring-Girard formulas for symmetric polynomials on spaces $\ell_p$

Authors

  • O.V. Handera-Kalynovska Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0003-1376-3763
  • V.V. Kravtsiv Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-7702-7071
https://doi.org/10.15330/cmp.16.2.407-413

Keywords:

symmetric polynomial on a Banach space, Waring-Girard formula, algebraic bases, combinatorial relation
Published online: 2024-10-10

Abstract

Classical Waring-Girard formulas gives a representation of elementary and complete symmetric polynomials through the power symmetric polynomials. In this paper, we propose some analogs of the Waring-Girard formulas in the case of spaces $\ell_p,$ where $1\le p<\infty$, and show an application of obtained formulas in combinatorics.

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How to Cite
(1)
Handera-Kalynovska, O.; Kravtsiv, V. The Waring-Girard Formulas for Symmetric Polynomials on Spaces $\ell_p$. Carpathian Math. Publ. 2024, 16, 407-413.