PARITY RESULTS for PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER of TIMES

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticle

Abstract

We consider the function f(n) that enumerates partitions of weight wherein each part appears an odd number of times. Chern ['Unlimited parity alternating partitions', Quaest. Math. (to appear)] noted that such partitions can be placed in one-to-one correspondence with the partitions of which he calls unlimited parity alternating partitions with smallest part odd. Our goal is to study the parity of in detail. In particular, we prove a characterisation of modulo 2 which implies that there are infinitely many Ramanujan-like congruences modulo 2 satisfied by the function The proof techniques are elementary and involve classical generating function dissection tools.

Original languageEnglish (US)
Pages (from-to)51-55
Number of pages5
JournalBulletin of the Australian Mathematical Society
Volume99
Issue number1
DOIs
StatePublished - Feb 1 2019
Externally publishedYes

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Keywords

  • congruences
  • generating functions
  • partitions

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