An extension to overpartitions of Rogers-Ramanujan identities for even moduli

Sylvie Corteel 1 Jeremy Lovejoy 2 Olivier Mallet 2
1 LRI - Laboratoire de Recherche en Informatique
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
Abstract : We investigate class of well-poised basic hypergeometric series $\tilde{J}_{k,i}(a;x;q)$, interpreting these series as generating functions for overpartitions defined by multiplicity conditions. We also show how to interpret the $\tilde{J}_{k,i}(a;1;q)$ as generating functions for overpartitions whose successive ranks are bounded, for overpartitions that are invariant under a certain class of conjugations, and for special restricted lattice paths. We highlight the cases $(a,q) \to (1/q,q)$, $(1/q,q^2)$, and $(0,q)$, where some of the functions $\tilde{J}_{k,i}(a;x;q)$ become infinite products. The latter case corresponds to Bressoud's family of Rogers-Ramanujan identities for even moduli.
Keywords : Partitions overpartitions Rogers-Ramanujan identities lattice paths
Type de document :
Communication dans un congrès
Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.141-150, 2006, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [24 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-01184702
Contributeur : Coordination Episciences Iam <>
Soumis le : lundi 17 août 2015 - 14:24:22
Dernière modification le : mardi 24 avril 2018 - 13:55:38
Document(s) archivé(s) le : mercredi 18 novembre 2015 - 12:08:52

Fichier

dmAG0107.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01184702, version 1

Collections

INSMI | UMR8623 | USPC | INRIA | TDS-MACS

Citation

Sylvie Corteel, Jeremy Lovejoy, Olivier Mallet. An extension to overpartitions of Rogers-Ramanujan identities for even moduli. Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.141-150, 2006, DMTCS Proceedings. 〈hal-01184702〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

183

Téléchargements de fichiers

107

Contact


archive-ouverte@inria.fr