UNIQUE DECIPHERABILITY IN THE ADDITIVE MONOID OF SETS OF NUMBERS

: Saarela A

Publisher: CAMBRIDGE UNIV PRESS

: 2011

RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications

: RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS

: RAIRO-THEOR INF APPL

: 2

: 45

: 2

: 225

: 234

: 10

: 0988-3754

DOI: https://doi.org/10.1051/ita/2011018

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.

rational set, sumset, Unique decipherability