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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
berndt@math.uiuc.edu
2Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
yee@math.psu.edu
Annals of Combinatorics 7 (4) p.409-423 December, 2003
AMS Subject Classification: 05A17, 11P81
Abstract:
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

References:

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