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Additive Systems and a Theorem of de Bruijn

Abstract This paper proves a theorem of de Bruijn that classifies additive systems for the nonnegative integers, that is, families A = (Ai)iεI of sets of nonnegative integers, each set containing 0, such that every nonnegative integer can be written uniquely in the form , with ai ε Ai for all i, and ai ≠for only finitely many i.