Title: Symmetries of decimation invariant sequences and digit sets
Authors: Barbé, André ×
von Haeseler, F #
Issue Date: Oct-2002
Publisher: Elsevier science bv
Series Title: Theoretical computer science vol:289 issue:1 pages:105-136
Abstract: A bi-infinite sequence is called p-decimation invariant if all p-decimations of it reproduce the sequence albeit with a shift. In this paper we discuss symmetry properties of decimation invariant sequences. A symmetry is a composition of a translation and a reflection. We establish the existence of translation invariant, i.e., periodic, decimation invariant sequences. Moreover, we prove that there exist decimation invariant sequences which are left-periodic and right-periodic, i.e., they are partially translation invariant. We present several criteria for the existence of decimation invariant sequences with additional periodicity properties. Finally, we discuss the existence of decimation invariant sequences that are invariant under reflections. Moreover, in passing we demonstrate that properties of decimation invariant sequences are linked with properties of certain digit sets. (C) 2002 Elsevier Science B.V. All rights reserved.
ISSN: 0304-3975
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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