English

Congruence properties of binary partition functions

Number Theory 2011-03-01 v1 Combinatorics

Abstract

Let A be a finite subset of the natural numbers containing 0, and let f(n) denote the number of ways to write n in the form ej2j\sum e_j2^j, where \ejA\e_j \in 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.

Keywords

Cite

@article{arxiv.1102.5355,
  title  = {Congruence properties of binary partition functions},
  author = {Katherine Anders and Melissa Dennison and Bruce Reznick and Jennifer Weber},
  journal= {arXiv preprint arXiv:1102.5355},
  year   = {2011}
}
R2 v1 2026-06-21T17:32:14.199Z