TY - JOUR

T1 - Ramanujan's lost notebook

T2 - Combinatorial proofs of identities associated with Heine's transformation or partial theta functions

AU - Berndt, Bruce C.

AU - Kim, Byungchan

AU - Yee, Ae Ja

N1 - Funding Information:
E-mail addresses: berndt@illinois.edu (B.C. Berndt), bkim4@illinois.edu (B. Kim), yee@math.psu.edu (A.J. Yee). 1 Research partially supported by grant H98230-07-1-0088 from the National Security Agency. 2 Research partially supported by National Science Foundation Grant DMS-0801184.

PY - 2010/10

Y1 - 2010/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77953806969&partnerID=8YFLogxK

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U2 - 10.1016/j.jcta.2009.07.005

DO - 10.1016/j.jcta.2009.07.005

M3 - Article

AN - SCOPUS:77953806969

VL - 117

SP - 957

EP - 973

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 7

ER -