Unique decipherability in the additive monoid of sets of numbers
Aleksi Saarela · RAIRO - Theoretical Informatics and Applications · 2011
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 and . 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.