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Overpartitions and the q-Bailey identity

Part of: Basic hypergeometric functions Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  28 May 2009

Sylvie Corteel  and
Jeremy Lovejoy
Sylvie Corteel
Affiliation:
Laboratoire de Recherche en Informatique, CNRS and Université Paris-Sud, Bâtiment 490, 91405 Orsay, France; Email: (corteel@lri.fr)
Jeremy Lovejoy
Affiliation:
CNRS, Laboratoire d'Informatique Algorithmique: Fondements et Applications, Université Denis Diderot—Paris 7, Case 7014, 75205 Paris Cedex 13, France; Email: (lovejoy@liafaffijussieu.fr)
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Abstract

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Using the framework of overpartitions, we give a combinatorial interpretation and proof of the q-Bailey identity. We then deduce from this identity a couple of facts about overpartitions. We show that the method of proof of the q-Bailey identity also applies to the (first) q-Gauss identity.

Keywords

partitionoverpartitionq-Bailey identitygeneralized Durfee square

MSC classification

Secondary: 11P81: Elementary theory of partitions 05A17: Partitions of integers 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 2 , June 2009 , pp. 297 - 306
Copyright
Copyright © Edinburgh Mathematical Society 2009