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Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules
We introduce a combinatorial way of calculating the Hilbert series of bigraded $S_n$-modules as a weighted sum over standard Young tableaux in the hook shape case. This method is based on Macdonald formula for Hall-Littlewood polynomial and extends the result of $A$. Garsia and $C$. Procesi for the Hilbert series …