Arithmetic properties of partitions with odd parts distinct

Michael D. Hirschhorn, James Allen Sellers

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

In this work, we consider the function pod(n), the number of partitions of an integer n wherein the odd parts are distinct (and the even parts are unrestricted), a function which has arisen in recent work of Alladi. Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan's congruences for the unrestricted partition function p(n). We prove a number of results for pod(n) including the following infinite family of congruences: for all α≥0 and n≥0.

Original languageEnglish (US)
Pages (from-to)273-284
Number of pages12
JournalRamanujan Journal
Volume22
Issue number3
DOIs
StatePublished - Apr 15 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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