The 'core' of symmetric homogeneous polynomial inequalities of degree four of three real variables

Abstract

In this paper we explore inequalities between symmetric homogeneous polynomials of degree four of three real variables and three nonnegative real variables. The main theorems describe the cases in which the smallest possible coefficient is not expressed by the other coefficients. The problem is resolved by introducing a parametric representation.

Mathematics Subject Classication (2010): 26D05.
Key words: Symmetric, homogeneous, polynomial, inequalities, degree four.