# A combinatorial model for the decomposition of multivariate polynomials rings as an $S_n$-module

Orellana Rosa

Abstract:

We consider the symmetric group $S_n$ module of the polynomial ring with $m$ sets of $n$ commuting variables and $m'$ sets of $n$ anti-commuting variables and calculate that the multiplicity of an irreducible indexed by the partition $\lambda$ (a partition of $n$) is the number of multiset tableaux of shape $\lambda$ satisfying certain ...More

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