Séminaire Lotharingien de Combinatoire, B08h (1984), 4 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1984, 229/S--08, p. 59-62.]

Heinz Lüneburg

Über symmetrische Polynome

Abstract. Let R be a commutative ring with a unit element and R[x(1),...,x(n)] be the polynomial ring in the variables x(1),...,x(n) with coefficients in R. Denote by S the subring of all symmetric polynomials in R[x(1),...,x(n)] and let E(n) be the set of all (n-1)-vectors e=(e(1),...,e(n-1)) such that each e(i) is between 0 and i. Each f in R[x(1),...,x(n)] can be expressed as a sum of monomials X(e) in x(2),...,x(n) whose powers belong to E(n) and whose coefficients S(e) belong to S. The purpose of this paper is to derive an algorithm that calculates the elements S(e) for each f.

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