Elementary proofs of parity results for 5-regular partitions

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticlepeer-review

80 Scopus citations


In a recent paper, Calkin et al. [N. Calkin, N. Drake, K. James, S. Law, P. Lee, D. Penniston and J. Radder, Divisibility properties of the 5-regular and 13-regular partition functions, Integers 8 (2008), #A60] used the theory of modular forms to examine 5-regular partitions modulo2 and 13-regular partitions modulo2 and3; they obtained and conjectured various results. In this note, we use nothing more than Jacobis triple product identity to obtain results for 5-regular partitions that are stronger than those obtained by Calkin and his collaborators. We find infinitely many Ramanujan-type congruences for b5(n), and we prove the striking result that the number of 5-regular partitions of the number n is even for at least 75% of the positive integers n.

Original languageEnglish (US)
Pages (from-to)58-63
Number of pages6
JournalBulletin of the Australian Mathematical Society
Issue number1
StatePublished - Feb 2010
Externally publishedYes


  • Congruences
  • Jacobis triple product identity
  • Partitions
  • Regular partitions


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