Geodesic
Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

Voir la notice de l'article provenant de la source Episciences

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. 
@article{DMTCS_2009_special_256_a26,
     author = {Yoo, Meesue},
     title = {Combinatorial {Formula} for the {Hilbert} {Series} of bigraded $S_n$-modules},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2704},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2704/}
}
TY  - JOUR
AU  - Yoo, Meesue
TI  - Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules
JO  - Discrete mathematics & theoretical computer science
PY  - 2009
VL  - DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2704/
DO  - 10.46298/dmtcs.2704
LA  - en
ID  - DMTCS_2009_special_256_a26
ER  - 
%0 Journal Article
%A Yoo, Meesue
%T Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules
%J Discrete mathematics & theoretical computer science
%D 2009
%V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2704/
%R 10.46298/dmtcs.2704
%G en
%F DMTCS_2009_special_256_a26
Yoo, Meesue. Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2704. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2704/

Cité par Sources :