Elementary proofs of various facts about 3-cores

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

Using elementary means, we derive an explicit formula for a3(n), the number of 3-core partitions of n, in terms of the prime factorization of 3n+1. Based on this result, we are able to prove several infinite families of arithmetic results involving a3(n), one of which specializes to the recent result of Baruah and Berndt which states that, for all n ≥ 0, a 3(4n+1)=a3(n).

Original languageEnglish (US)
Pages (from-to)507-512
Number of pages6
JournalBulletin of the Australian Mathematical Society
Volume79
Issue number3
DOIs
StatePublished - Jun 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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