1预备知识设u=x+y+z,v=xy+xz+yz,w=xyz,则u,v,w称为关于x,y,z的基本对称多项式.从线性代数中知道,每一个三元n次齐次的对称多项式f(x,y,z)均可唯一地表示成关于u,v,w的多项式.例如:∑x2=u2-2v,∑x3=u3-3uv,∑(x2y+xy2)=uv-3w.其中∑表示循环求和,下同.2引理(Schur不等式)若x,y, 1 We know that u, v, w are the basic symmetric polynomials about x, y, z, u = x + y + z, v = xy + xz + yz and w = xyz. From the linear algebra, A symmetric polynomial f (x, y, z) of a ternary n-times homogeneous can be uniquely expressed as a polynomial on u, v, w For example: Σx2 = u2-2v, Σx3 = u3-3uv, Σ (x2y + xy2) = uv-3w, where Σ denotes the sum of cycles, and the same holds for the following (Schur’s inequality) if x, y,