# 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.
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https://hal.inria.fr/hal-01184702
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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, ⟨10.46298/dmtcs.3498⟩. ⟨hal-01184702⟩

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