### Abstract

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 ∑ε_{j}2^{j}, where ε_{j}∈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 language | English (US) |
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Pages (from-to) | 15-26 |

Number of pages | 12 |

Journal | Annals of Combinatorics |

Volume | 17 |

Issue number | 1 |

DOIs | |

State | Published - Feb 11 2013 |

### Keywords

- Stern sequence
- digital representations
- partitions

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

Anders, K., Dennison, M., Lansing, J. W., & Reznick, B. (2013). Congruence Properties of Binary Partition Functions.

*Annals of Combinatorics*,*17*(1), 15-26. https://doi.org/10.1007/s00026-013-0188-3