Meesue Yoo - Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules

dmtcs:2704 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2704
Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modulesArticle

Authors: Meesue Yoo 1

  • 1 Department of Mathematics [Philadelphia]

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 when $q=0$. Moreover, we give the way of associating the fillings giving the monomial terms of Macdonald polynomials to the standard Young tableaux.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: combinatorial formula,Hilbert series,Garsia-Haiman modules,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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