The Ring of Multisymmetric Functions

@inproceedings{Vaccarino2005TheRO,
  title={The Ring of Multisymmetric Functions},
  author={Francesco Vaccarino},
  year={2005}
}
Abstract. Let R be a commutative ring and let n, m be two positive integers. Let AR(n, m) be the polynomial ring in the commuting independent variables xi(j) with i = 1, . . . , m ; j = 1, . . . , n and coefficients in R. The symmetric group on n letters Sn acts on AR(n, m) by means of σ(xi(j)) = xi(σ(j)) for all σ ∈ Sn and i = 1, . . . , m ; j = 1, . . . , n. Let us denote by AR(n, m) Sn the ring of invariants for this action: its elements are usually called multisymmetric functions and they… CONTINUE READING

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