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: [email protected] (B.C. Berndt), [email protected] (B. Kim), [email protected] (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.
KW - Combinatorial proofs
KW - Heine's transformation
KW - Integer partitions
KW - Partial theta functions
KW - Ramanujan's lost notebook
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
SN - 0097-3165
VL - 117
SP - 957
EP - 973
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 7
ER -