A New Class of Relations for Homogeneous Symmetric Polynomials

TL;DR

This paper extends recently introduced relations for Bernoulli symmetric polynomials to all homogeneous symmetric polynomials, revealing new nonlinear relations for Bernoulli numbers and broadening understanding of their algebraic structure.

Contribution

It generalizes specific relations from Bernoulli symmetric polynomials to all homogeneous symmetric polynomials, uncovering new nonlinear relations for Bernoulli numbers.

Findings

Relations valid for all homogeneous symmetric polynomials

Discovery of new nonlinear relations for Bernoulli numbers

Broader algebraic framework for Bernoulli-related polynomials

Abstract

Recently we introduced a new class of relations for Bernoulli symmetric polynomials. This manuscript shows that these relations are valid for arbitrary homogeneous symmetric polynomial. Analysis of these relations leads to the discovery of a new type of nonlinear relations for the Bernoulli numbers.