A Combinatorial Formula for the Hilbert Series of Bigraded Sn-Modules
نویسنده
چکیده
We prove a combinatorial formula for the Hilbert series of the Garsia-Haiman bigraded Sn-modules as weighted sums over standard Young tableaux in the hook shape case. This method is based on the combinatorial formula of Haglund, Haiman and Loehr for the Macdonald polynomials and extends the result of A. Garsia and C. Procesi for the Hilbert series when q = 0. Moreover, we construct an association of the fillings giving the monomial terms of Macdonald polynomials with the standard Young tableaux.
منابع مشابه
Combinatorial Formula for the Hilbert Series of bigraded Sn-modules
We introduce a combinatorial way of calculating the Hilbert series of bigraded Sn-modules as a weighted sum over standard Young tableaux in the hook shape case. This method is based on Macdonald formula for HallLittlewood polynomial and extends the result of A. Garsia and C. Procesi for the Hilbert series when q = 0. Moreover, we give the way of associating the fillings giving the monomial term...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010