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

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 $\ell_p(\mathbb{C}^s),$ $1\leq p1.$ In this paper, we derive analogs of the Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials and explore their combinatorial applications.

Keywords

• block-symmetric polynomial
• block-supersymmetric polynomial
• waring-girard formula
• algebraic bases
• combinatorial relation