A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
UNIQUE DECIPHERABILITY IN THE ADDITIVE MONOID OF SETS OF NUMBERS
Tekijät: Saarela A
Kustantaja: CAMBRIDGE UNIV PRESS
Julkaisuvuosi: 2011
Lehti: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications
Tietokannassa oleva lehden nimi: RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS
Lehden akronyymi: RAIRO-THEOR INF APPL
Numero sarjassa: 2
Vuosikerta: 45
Numero: 2
Aloitussivu: 225
Lopetussivu: 234
Sivujen määrä: 10
ISSN: 0988-3754
DOI: https://doi.org/10.1051/ita/2011018
Tiivistelmä
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.
Avainsanat:
rational set, sumset, Unique decipherability
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