Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials

V. V. Kravtsiv; P. Y.  Dolishniak; R. Y. Stakhiv

doi:10.30970/ms.63.2.210-220

V. V. Kravtsiv Vasyl Stefanyk Carpathian National University, Ivano-Frankivsk, Ukraine
P. Y. Dolishniak Vasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
R. Y. Stakhiv Vasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

DOI: https://doi.org/10.30970/ms.63.2.210-220

Keywords: block-symmetric polynomial, block-supersymmetric polynomial, Waring-Girard formula, algebraic bases, combinatorial relation

Abstract

This paper investigates the structure and properties of block-symmetric and block-super\-symmetric polynomials in Banach spaces. The study extends classical symmetric polynomial results to infinite-dimensional settings, particularly in sequence spaces such as $\ell_p(\mathbb{C}^s),$ $1\leq p<\infty$ and spaces of two-sided absolutely summing series of vectors in $\mathbb{C}^s$ for some positive integer $s>1.$ In this paper, we derive analogs of the Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials and explore their combinatorial applications.

Author Biographies

V. V. Kravtsiv, Vasyl Stefanyk Carpathian National University, Ivano-Frankivsk, Ukraine

Vasyl Stefanyk Carpathian National University,
Ivano-Frankivsk, Ukraine

P. Y. Dolishniak, Vasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

Vasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

R. Y. Stakhiv, Vasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

Vasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

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