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arXiv · 1301.6208

Additive systems and a theorem of de Bruijn

Melvyn B. Nathanson
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Abstract

This paper gives a complete proof of a theorem of de Bruijn that classifies additive systems for the nonnegative integers, that is, families $\mca = (A_i)_{i\in I}$ of sets of nonnegative integers, each set containing 0, such that every nonnegative integer can be written uniquely in the form $\sum_{i\in I} a_i$ with $a_i \in A_i$ for all $i$ and $a_i \neq 0$ for only finitely many $i$. All indecomposable additive systems are determined.

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Melvyn B. Nathanson. 2013-01-26. Additive systems and a theorem of de Bruijn. https://arxiv.org/abs/1301.6208

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