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Unique Decipherability in the Additive Monoid of Sets of Numbers

Aleksi Saarela, Unique Decipherability in the Additive Monoid of Sets of Numbers. RAIRO - Theoretical Informatics and Applications 45(2), 225-234, 2011.

http://dx.doi.org/10.1051/ita/2011018

Abstract:

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.

BibTeX entry:

@ARTICLE{jSaarela_Aleksi11a,
  title = {Unique Decipherability in the Additive Monoid of Sets of Numbers},
  author = {Saarela, Aleksi},
  journal = {RAIRO - Theoretical Informatics and Applications},
  volume = {45},
  number = {2},
  pages = {225-234},
  year = {2011},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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