Multisymmetric polynomials in dimension three

The polarizations of one relation of degree five and two relations of degree six minimally generate the ideal of relations among a minimal generating system of the algebra of multisymmetric polynomials in an arbitrary number of three-dimensional vector variables. In the general case of n-dimensional vector variables, a relation of degree 2n among the polarized power sums is presented such that it is not contained in the ideal generated by lower degree relations. (C) 2012 Elsevier Inc. All rights reserved.