Unique decipherability in the additive monoid of sets of numbers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 2, pp. 225-234.

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.

DOI : https://doi.org/10.1051/ita/2011018
Classification : 68R05,  68Q45
Mots clés : unique decipherability, rational set, sumset
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author = {Saarela, Aleksi},
title = {Unique decipherability in the additive monoid of sets of numbers},
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Saarela, Aleksi. Unique decipherability in the additive monoid of sets of numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 2, pp. 225-234. doi : 10.1051/ita/2011018. http://www.numdam.org/articles/10.1051/ita/2011018/

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