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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
##### Keywords:
unique decipherability; rational set; sumset
Full Text:
##### References:
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