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A Note on the Positivity of the Even Degree Complete Homogeneous Symmetric Polynomials

  • Ionel RovenţaEmail author
  • Laurenţiu Emanuel Temereancă
Article
  • 57 Downloads

Abstract

This article deals with the positivity of a nice family of symmetric polynomials, namely complete homogeneous symmetric polynomials. We are able to give a positive answer to a question arising in Tao (https://terrytao.wordpress.com/2017/08/06/schur-convexity-and-positive-definiteness-of-the-even-degree-complete-homogeneous-symmetric-polynomials/, 2017). Our strategy follows two different ideas, one of them based on a Schur-convexity argument and the other one uses a method with divided differences. Several Newton’s type inequalities are also discussed.

Keywords

Symmetric polynomials divided differences and Schur-convexity 

Mathematics Subject Classification

Primary 26B25 Secondary 26D05 05E05 

Notes

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ionel Rovenţa
    • 1
    Email author
  • Laurenţiu Emanuel Temereancă
    • 2
  1. 1.Department of MathematicsUniversity of CraiovaCraiovaRomania
  2. 2.Department of Applied MathematicsUniversity of CraiovaCraiovaRomania

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