论文标题
通用的muirhead不平等和非负回路的对称总和
A Generalized Muirhead Inequality and Symmetric Sums of Nonnegative Circuits
论文作者
论文摘要
电路多项式是真实多项式的非阴性证书，可以通过对算术和几何方式的经典不平等的概括来得出。在本文中，我们表明，对称真实多项式的类似非负性可以通过对经典的穆赫黑德不平等的概括来认证。此外，我们表明，当且仅当它满足所述概括性的穆赫德条件时，非负对称多项式将分解为非负电路多项式的总和。后者以一种缩短，更基本的方式重新提供了Moustrou，Naumann，Riener，Theobald和Verdure的结果。
Circuit polynomials are a certificate of nonnegativity for real polynomials, which can be derived via a generalization of the classical inequality of arithmetic and geometric means. In this article, we show that similarly nonnegativity of symmetric real polynomials can be certified via a generalization of the classical Muirhead inequality. Moreover, we show that a nonnegative symmetric polynomial admits a decomposition into sums of nonnegative circuit polynomials if and only if it satisfies said generalized Muirhead condition. The latter re-proves a result by Moustrou, Naumann, Riener, Theobald, and Verdure for the case of the symmetric group in a shortened and more elementary way.
