The center of z[s_n+1] is the set of symmetric polynomials in n commuting transposition-sums

Let S_n+1 be the symmetric group on the n + 1 symbols 0,1,2,., n. We show that the center of the group-ring Z[S_n+1] coincides with the set of symmetric polynomials with integral coefficients in the n elements s₁,…s_n ϵ Z[S_n+1], where s_k = 㨰_≤i≤k(i, k) is a surn of k transpositions, k = 1,., n. In particular, every conjugacy-class-sum of S_n+1, is a symmetric polynomial in s₁,., s_n.