Arithmetic properties of partitions with even parts distinct

George E. Andrews, Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticle

58 Scopus citations

Abstract

In this work, we consider the function ped(n), the number of partitions of an integer n wherein the even parts are distinct (and the odd parts are unrestricted). Our goal is to consider this function from an arithmetical point of view in the spirit of Ramanujan's congruences for the unrestricted partition function p(n). We prove a number of results for ped(n) including the following: For all n≥0, ped(9n+4) ≡ 0 (mod 4) and ped(9n+7)≡ (mod 12). Indeed, we compute appropriate generating functions from which we deduce these congruences and find, in particular, the surprising result that We also show that ped(n) is divisible by 6 at least 1/6 of the time.

Original languageEnglish (US)
Pages (from-to)169-181
Number of pages13
JournalRamanujan Journal
Volume23
Issue number1
DOIs
StatePublished - Dec 1 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Arithmetic properties of partitions with even parts distinct'. Together they form a unique fingerprint.

  • Cite this