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Unique decipherability in the additive monoid of sets of numbers. (English) Zbl 1218.68108
Summary: Sets of integers form a monoid, where the product of two sets \(A\) and \(B\) is defined as the set containing \(a+b\) for all \(a \in A\) and \(b \in B\). We give a characterization of when a family of finite sets is a code in this monoid, that is when the sets do not satisfy any nontrivial relation. We also extend this result for some infinite sets, including all infinite rational sets.

MSC:
68R05 Combinatorics in computer science
68Q45 Formal languages and automata
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