Congruence Properties of Binary Partition Functions |
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| Authors: | Katherine Anders Melissa Dennison Jennifer Weber Lansing Bruce Reznick |
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| Institution: | 1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street (MC-382), Urbana, IL, 61801, USA
2. Department of Mathematics and Computer Science, Baldwin-Wallace College, Berea, OH, 44017, USA
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| Abstract: | Let ${\mathcal{A}}$ be a finite subset of ${\mathbb{N}}$ containing 0, and let f (n) denote the number of ways to write n in the form ${\sum \varepsilon _{j}2^{j}}$ , where ${\varepsilon _{j} \epsilon \mathcal{A}}$ . We show that there exists a computable ${T = T (\mathcal{A})}$ 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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