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

Research output: Contribution to journalArticlepeer-review

17 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 languageEnglish (US)
Pages (from-to)957-973
Number of pages17
JournalJournal of Combinatorial Theory. Series A
Volume117
Issue number7
DOIs
StatePublished - Oct 2010

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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