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

Part of: Algebraic combinatorics Partial differential equations

Published online by Cambridge University Press:  02 April 2025

Shuqi Hu ,
Changyu Ren  and
Ziyi Wang
Shuqi Hu
Affiliation:
School of Mathematical Science, Jilin University, Changchun, Jilin Province, 130012, China (husq21@mails.jlu.edu.cn)
Changyu Ren*
Affiliation:
School of Mathematical Science, Jilin University, Changchun, China (rency@jlu.edu.cn) (corresponding author)
Ziyi Wang
Affiliation:
School of Mathematical Science, Jilin University, Changchun, China (ziyiw23@mails.jlu.edu.cn)
*
*Corresponding author.
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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.

Keywords

Hessian equationNewton inequalityMaclaurin inequalityprimitive symmetric function

MSC classification

Primary: 05E05: Symmetric functions and generalizations
Secondary: 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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