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Journal of the London Mathematical Society 2004 69(3):562-574; doi:10.1112/S0024610704005216
© 2004 by London Mathematical Society
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© The London Mathematical Society

Overpartition Theorems of the Rogers–Ramanujan Type

Jeremy Lovejoy

CNRS, LABRI, Université Bordeaux I 351 Cours de la Libération, 33405 Talence Cedex, France, lovejoy{at}labri.fr

Received 11 July 2003.

One-parameter overpartition-theoretic analogues are given of two classical families of partition identities: Andrews' combinatorial generalization of the Gollnitz–Gordon identities and a theorem of Andrews and Santos on partitions with attached odd parts. Geometric counterparts arising from multiple q-series identities are also discussed. These involve representations of overpartitions in terms of generalized Frobenius partitions.


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