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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

Berndt, Bruce C.¹  Kim, Byungchan¹  Yee, Ae Ja² 

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: Integer partitions;    Combinatorial proofs;    Heine's transformation;    Partial theta functions;    Ramanujan's lost notebook;   

DOI  :  10.1016/j.jcta.2009.07.005

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free