Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions |
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| Authors: | Bruce C. Berndt Byungchan Kim |
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| Affiliation: | a Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA
b Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA |
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| Abstract: | Combinatorial proofs are given for certain entries in Ramanujan's lost notebook. Bijections of Sylvester, Franklin, and Wright, and applications of Algorithm Z of Zeilberger are employed. A new bijection, involving the new concept of the parity sequence of a partition, is used to prove one of Ramanujan's fascinating identities for a partial theta function. |
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| Keywords: | Integer partitions Combinatorial proofs Heine's transformation Partial theta functions Ramanujan's lost notebook |
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