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arXiv · 0710.0470

A minimal set of generators for the ring of multisymmetric functions

David Rydh
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Abstract

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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David Rydh. 2007-10-02. A minimal set of generators for the ring of multisymmetric functions. https://doi.org/10.5802/aif.2312

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