Congruence Properties of Binary Partition Functions

Katherine Anders, Melissa Dennison, Jennifer Weber Lansing, Bruce Reznick

Research output: Contribution to journalArticlepeer-review


Let A be a finite subset of N containing 0, and let f (n) denote the number of ways to write n in the form ∑εj2j, where εj∈A. We show that there exists a computable T = T(A) so that the sequence (f (n) mod 2) is periodic with period T. Variations and generalizations of this problem are also discussed.

Original languageEnglish (US)
Pages (from-to)15-26
Number of pages12
JournalAnnals of Combinatorics
Issue number1
StatePublished - Mar 2013


  • Stern sequence
  • digital representations
  • partitions

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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