(this is actually an identity of polynomials in , because after the elementary symmetric polynomials become zero). Multiplying this by the generating function for the complete homogeneous symmetric polynomials, one obtains the constant series 1, and the relation between the elementary and complete homogeneous polynomials follows from comparing coefficients of . A somewhat more direct way to understand that relation, is to consider the contributions in the summation involving a fixed monomial of degree . For any subset of the variables appearing with nonzero exponent in the monomial, there is a contribution involving the product of those variables as term from , where , and the monomial from ; this contribution has coefficient . The relation then follows from the fact that