Geodesic
A combinatorial model for the decomposition of multivariate polynomial rings as \(S_n\)-modules
Rosa Orellana1 ; Michael Zabrocki
1Dartmouth College
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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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 show 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 column and row strict conditions. We also present a finite generating set for the ring of $S_n$ invariant polynomials of this ring.
DOI : 10.37236/8935
Classification : 05E05, 05E10, 20C30
Mots-clés : symmetric group \(S_n\)-module, finite generating set

Rosa Orellana  1   ; Michael Zabrocki 

1 Dartmouth College 
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     author = {Rosa Orellana and Michael Zabrocki},
     title = {A combinatorial model for the decomposition of multivariate polynomial rings as {\(S_n\)-modules}},
     journal = {The electronic journal of combinatorics},
     year = {2020},
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     number = {3},
     doi = {10.37236/8935},
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Rosa Orellana; Michael Zabrocki. A combinatorial model for the decomposition of multivariate polynomial rings as \(S_n\)-modules. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/8935

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