Skip to Main content Skip to Navigation
Conference papers

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

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.
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download

https://hal.inria.fr/hal-01184702
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, August 17, 2015 - 2:24:22 PM
Last modification on : Thursday, July 8, 2021 - 3:49:52 AM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:08:52 PM

File

dmAG0107.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01184702, version 1

Citation

Sylvie Corteel, Jeremy Lovejoy, Olivier Mallet. An extension to overpartitions of Rogers-Ramanujan identities for even moduli. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.141-150. ⟨hal-01184702⟩

Share

Metrics

Record views

353

Files downloads

793