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Combinatorial Proofs of Identities in Ramanujan's Lost Notebook Associated with the Rogers-Fine Identity and False Theta Functions
Bruce C. Berndt1 and Ae Ja Yee2
1Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA
2Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
Annals of Combinatorics 7 (4) p.409-423 December, 2003
AMS Subject Classification: 05A17, 11P81
Ramanujan's lost notebook contains several identities arising from the Rogers-Fine identity and/or Rogers' false theta functions. Combinatorial proofs for many of these identities are given.
Keywords: partitions of integers, Ramanujan's lost notebook, false theta functions, Rogers-Fine identity, Ferrers graphs, Franklin's involution, MacMahon's k-modular partitions


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