A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version)
International audience A special case of Haiman's identity [Invent. Math. 149 (2002), pp. 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in...
Main Author: | |
---|---|
Other Authors: | , , , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2011
|
Subjects: | |
Online Access: | https://hal.inria.fr/hal-01215103 https://hal.inria.fr/hal-01215103/document https://hal.inria.fr/hal-01215103/file/dmAO0140.pdf |
id |
ftccsdartic:oai:HAL:hal-01215103v1 |
---|---|
record_format |
openpolar |
spelling |
ftccsdartic:oai:HAL:hal-01215103v1 2023-05-15T16:51:16+02:00 A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version) Haglund, J. Department of Mathematics Philadelphia University of Pennsylvania Philadelphia Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel Reykjavik, Iceland 2011 https://hal.inria.fr/hal-01215103 https://hal.inria.fr/hal-01215103/document https://hal.inria.fr/hal-01215103/file/dmAO0140.pdf en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS hal-01215103 https://hal.inria.fr/hal-01215103 https://hal.inria.fr/hal-01215103/document https://hal.inria.fr/hal-01215103/file/dmAO0140.pdf info:eu-repo/semantics/OpenAccess ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215103 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.445-456 Hilbert series diagonal coinvariants [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] info:eu-repo/semantics/conferenceObject Conference papers 2011 ftccsdartic 2020-12-25T18:15:03Z International audience A special case of Haiman's identity [Invent. Math. 149 (2002), pp. 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in $q,t$. In this paper we show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman's formula for the Hilbert series into an explicit polynomial in $q,t$ with integer coefficients. We also provide an equivalent formula for the Hilbert series as the constant term in a multivariate Laurent series. Un cas spécial de l'identité de Haiman [Invent. Math. \textbf149 (2002), pp. 371–407] pour le caractère de l'anneau quotient des coinvariants diagonaux sous l'action du groupe symétrique fournit une formule pour la série de Hilbert bigraduée comme somme de fonctions rationnelles en q,t. Dans cet article nous montrons comment une identité de sommation de Garsia et Zabrocki pour les coefficients de Pieri des polynômes de Macdonald peut être utilisée pour transformer la formule de Haiman pour la série de Hilbert en un polynôme explicite en q,t à coefficients entiers. Nous présentons également une formule équivalente pour la série de Hilbert comme terme constant d'une série de Laurent multivariée. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
Hilbert series diagonal coinvariants [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
spellingShingle |
Hilbert series diagonal coinvariants [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Haglund, J. A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version) |
topic_facet |
Hilbert series diagonal coinvariants [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
description |
International audience A special case of Haiman's identity [Invent. Math. 149 (2002), pp. 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in $q,t$. In this paper we show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman's formula for the Hilbert series into an explicit polynomial in $q,t$ with integer coefficients. We also provide an equivalent formula for the Hilbert series as the constant term in a multivariate Laurent series. Un cas spécial de l'identité de Haiman [Invent. Math. \textbf149 (2002), pp. 371–407] pour le caractère de l'anneau quotient des coinvariants diagonaux sous l'action du groupe symétrique fournit une formule pour la série de Hilbert bigraduée comme somme de fonctions rationnelles en q,t. Dans cet article nous montrons comment une identité de sommation de Garsia et Zabrocki pour les coefficients de Pieri des polynômes de Macdonald peut être utilisée pour transformer la formule de Haiman pour la série de Hilbert en un polynôme explicite en q,t à coefficients entiers. Nous présentons également une formule équivalente pour la série de Hilbert comme terme constant d'une série de Laurent multivariée. |
author2 |
Department of Mathematics Philadelphia University of Pennsylvania Philadelphia Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel |
format |
Conference Object |
author |
Haglund, J. |
author_facet |
Haglund, J. |
author_sort |
Haglund, J. |
title |
A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version) |
title_short |
A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version) |
title_full |
A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version) |
title_fullStr |
A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version) |
title_full_unstemmed |
A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version) |
title_sort |
polynomial expression for the hilbert series of the quotient ring of diagonal coinvariants (condensed version) |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
https://hal.inria.fr/hal-01215103 https://hal.inria.fr/hal-01215103/document https://hal.inria.fr/hal-01215103/file/dmAO0140.pdf |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215103 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.445-456 |
op_relation |
hal-01215103 https://hal.inria.fr/hal-01215103 https://hal.inria.fr/hal-01215103/document https://hal.inria.fr/hal-01215103/file/dmAO0140.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766041382693109760 |