Newton-Maclaurin type inequalities for linear combinations of elementary symmetric functions

TL;DR

This paper extends classical Newton-Maclaurin inequalities to a broader class of functions formed by linear combinations of elementary symmetric functions, providing new theoretical insights.

Contribution

It introduces generalized inequalities for linear combinations of elementary symmetric functions, broadening the scope of classical symmetric polynomial inequalities.

Findings

Established Newton-Maclaurin type inequalities for these functions

Extended classical inequalities to new classes of symmetric functions

Provided theoretical foundations for further research in symmetric polynomial inequalities

Abstract

In this paper, we establish Newton-Maclaurin type inequalities for functions arising from linear combinations of primitively symmetric polynomials. This generalization extends the classical Newton-Maclaurin inequality to a broader class of functions.