Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions

Bruce C. Berndt; Byungchan Kim; Ae Ja Yee

doi:10.1016/j.jcta.2009.07.005

Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions

Bruce C. Berndt
, Byungchan Kim
, Ae Ja Yee

School of Natural Sciences

University of Illinois at Urbana-Champaign
Pennsylvania State University

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

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.

Original language	English
Pages (from-to)	957-973
Number of pages	17
Journal	Journal of Combinatorial Theory. Series A
Volume	117
Issue number	7
DOIs	https://doi.org/10.1016/j.jcta.2009.07.005
State	Published - Oct 2010

Keywords

Combinatorial proofs
Heine's transformation
Integer partitions
Partial theta functions
Ramanujan's lost notebook

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10.1016/j.jcta.2009.07.005

Cite this

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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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KW - Combinatorial proofs

KW - Heine's transformation

KW - Integer partitions

KW - Partial theta functions

KW - Ramanujan's lost notebook

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Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions

Abstract

Keywords

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