Parity in partition identities

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Abstract

This paper considers a variety of parity questions connected with classical partition identities of Euler, Rogers, Ramanujan and Gordon. We begin by restricting the partitions in the Rogers-Ramanujan-Gordon identities to those wherein even parts appear an even number of times. We then take up questions involving sequences of alternating parity in the parts of partitions. This latter study leads to: (1) a bi-basic q-binomial theorem and q-binomial series, (2) a new interpretation of the Rogers-Ramanujan identities, and (3) a new natural interpretation of the fifth-order mock theta functions f0(q) along with a new proof of the Hecke-type series representation.

Original languageEnglish (US)
Pages (from-to)45-90
Number of pages46
JournalRamanujan Journal
Volume23
Issue number1
DOIs
StatePublished - Dec 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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