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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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