Arithmetic properties of overpartitions into odd parts

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

In this article, we consider various arithmetic properties of the function po(n) which denotes the number of overpartitions of n using only odd parts. This function has arisen in a number of recent papers, but in contexts which are very different from overpartitions. We prove a number of arithmetic results including several Ramanujan-like congruences satisfied by p o(n) and some easily-stated characterizations of po(n) modulo small powers of two. For example, it is proven that, for n≥1, p o(n) ≡ 0 (mod 4) if and only if n is neither a square nor twice a square.

Original languageEnglish (US)
Pages (from-to)353-367
Number of pages15
JournalAnnals of Combinatorics
Volume10
Issue number3
DOIs
StatePublished - Dec 2006
Externally publishedYes

Keywords

  • Congruence
  • Odd parts
  • Overpartition

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