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

被引：0
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作者：
Ionel Rovenţa
Laurenţiu Emanuel Temereancă
机构：
[1] University of Craiova,Department of Mathematics
[2] University of Craiova,Department of Applied Mathematics
来源：
Mediterranean Journal of Mathematics | 2019年 / 16卷
关键词：
Symmetric polynomials; divided differences and Schur-convexity; Primary 26B25; Secondary 26D05; 05E05;
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摘要：
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.
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