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arXiv · 1102.5355

Congruence properties of binary partition functions

Katherine Anders·Melissa Dennison·Bruce Reznick·Jennifer Weber
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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 $\sum e_j2^j$, where $\e_j \in A$. 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.

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Katherine Anders, Melissa Dennison, Bruce Reznick, Jennifer Weber. 2011-02-25. Congruence properties of binary partition functions. https://arxiv.org/abs/1102.5355

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