... 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) ... is known that [M] each of the sets {hλ}, {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] ... product, we expand G and uh3eu(h1+h2)in terms of the powersums, and use the property pλ,pµ = z(λ)δλ,µ of the inner product, the adjoint action tomultiplication by pj, and Taylor’s...