A proof of Muirhead’s Inequality

I’ve been reading Thomas Mildorf’s Olympiad Inequalities, and trying to prove the 12 Theorems stated at the beginning. I’m recording my proof of Muirhead’s Inequality below. Although it is probably known to people working in this area, I could not find it on the internet. Muirhead’s Inequality states the following: if the sequence majorizes theContinue reading “A proof of Muirhead’s Inequality”