Elementary proofs of parity results for 5-regular partitions

Michael D. Hirschhorn, James Allen Sellers

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

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
Volume81
Issue number1
DOIs
StatePublished - Feb 1 2010

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Parity
Partition
Triple product
Integer
Divisibility
Modular Forms
Ramanujan
Partition Function
Congruence

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Hirschhorn, Michael D. ; Sellers, James Allen. / Elementary proofs of parity results for 5-regular partitions. In: Bulletin of the Australian Mathematical Society. 2010 ; Vol. 81, No. 1. pp. 58-63.
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Elementary proofs of parity results for 5-regular partitions. / Hirschhorn, Michael D.; Sellers, James Allen.

In: Bulletin of the Australian Mathematical Society, Vol. 81, No. 1, 01.02.2010, p. 58-63.

Research output: Contribution to journalArticle

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