Sylvie Corteel ; Jeremy Lovejoy ; Olivier Mallet - An extension to overpartitions of Rogers-Ramanujan identities for even moduli

dmtcs:3498 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3498
An extension to overpartitions of Rogers-Ramanujan identities for even moduliConference paper

Authors: Sylvie Corteel 1; Jeremy Lovejoy 2; Olivier Mallet 2

  • 1 Laboratoire de Recherche en Informatique
  • 2 Laboratoire d'informatique Algorithmique : Fondements et Applications

We investigate class of well-poised basic hypergeometric series ˜Jk,i(a;x;q), interpreting these series as generating functions for overpartitions defined by multiplicity conditions. We also show how to interpret the ˜Jk,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)(1/q,q), (1/q,q2), and (0,q), where some of the functions ˜Jk,i(a;x;q) become infinite products. The latter case corresponds to Bressoud's family of Rogers-Ramanujan identities for even moduli.


Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: Partitions,overpartitions,Rogers-Ramanujan identities,lattice paths,[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

Consultation statistics

This page has been seen 246 times.
This article's PDF has been downloaded 243 times.