We present a method to prove an inequality concerning a linear combination of symmetric monomial functions. This is based on Muirhead’s inequality combining with a graph theoretical setting. As an application we prove some interesting inequalities motivated from extremal combinatorics.

中文翻译：

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扩展缪尔黑德的不等式

我们提出了一种方法来证明关于对称单项函数的线性组合的不等式。这是基于 Muirhead 不等式结合图形理论设置。作为一个应用，我们证明了一些由极值组合引发的有趣的不等式。