A1 Refereed original research article in a scientific journal
UNIQUE DECIPHERABILITY IN THE ADDITIVE MONOID OF SETS OF NUMBERS
Authors: Saarela A
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2011
Journal: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications
Journal name in source: RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS
Journal acronym: RAIRO-THEOR INF APPL
Number in series: 2
Volume: 45
Issue: 2
First page : 225
Last page: 234
Number of pages: 10
ISSN: 0988-3754
DOI: https://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 vertical bar b for all a is an element of A and b is an element of 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.
Sets of integers form a monoid, where the product of two sets A and B is defined as the set containing a vertical bar b for all a is an element of A and b is an element of 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.
Keywords:
rational set, sumset, Unique decipherability
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