On the parity of partition functions

Bruce C. Berndt, Ae Ja Yee, Alexandru Zaharescu

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Let S denote a subset of the positive integers, and let pS(n) be the associated partition function, that is, pS(n) denotes the number of partitions of the positive integer n into parts taken from S. Thus, if S is the set of positive integers, then pS(n) is the ordinary partition function p(n). In this paper, working in the ring of formal power series in one variable over the field of two elements Z/2Z, we develop new methods for deriving lower bounds for both the number of even values and the number of odd values taken by pS(n), for n ≤ N. New very general theorems are obtained, and applications are made to several partition functions.

Original languageEnglish (US)
Pages (from-to)437-459
Number of pages23
JournalInternational Journal of Mathematics
Volume14
Issue number4
DOIs
StatePublished - Jun 1 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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