A minimal set of generators for the ring of multisymmetric functions

Details A minimal set of generators for the ring of multisymmetric functions A minimal set of generators for the ring of multisymmetric functions

2007-10-02

arxiv.org/abs/0710.0470v1

Mathematics

Commutative Algebra

25 pages, to be published in Ann. Inst. Fourier

Scientific paper

The purpose of this article is to give, for any commutative ring A, an explicit minimal set of generators for the ring of multisymmetric functions TS^d_A(A[x_1,...,x_r]) as an A-algebra. In characteristic zero, i.e. when A is an algebra over the rational numbers, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously obtained by Fleischmann.

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