... {mλ},and{pλ},whereλ ranges over allpartitions of n, is a basis of the vector space over of symmetric functions homogeneous of degree n.15References[G] I. Gessel, Symmetric functions and P-recursiveness,J.CombinatorialTheory53 ... is equal to the number of sequences over {0, 1, 2, 3} of length n with n − l(α) occurrences of 0, m1(α) occurrences of 1, m2(α) occurrences of 2 and one occurrence of 3 (as specified by P3).12(3) ... sequence of positive integers, we let hλdenote hλ1hλ2···hλk. The weight of λ is |λ| :=iλi.The monomial symmetric function mλis the sum of all distinct monomials of the formxλ1i1···xλkik,wherei1,...