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In this article we will discuss a new type of notation for homogenous polynomials of $3$ variables, and its applications in solving Olympiad inequalities using the AM-GM inequality, Muirhead’s Inequality, and Schur’s Inequality. I suggest reading [1] first for a clearer explantion on the mechanics of this notation. This article is more focused on the applications to Olympiad inequalities

Beginning template for the 2015 Mathematical Contest in Modeling, http://www.comap.com/undergraduate/contests/.
This template will place the correct header on each page and reserves the first page for the required model summary.
All directions and instructions copied directly from the contest instructions.