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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 S 1, ..., S n e Z [S n+1 ], where S k = Σ 0≤i≤k (i,k) is a sum of k transposition k = 1,..., n. In particular, every conjugacy-class-sum of S n+1 is a symmetric polynomial in S 1 ,.., S n

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