Comparison of Coverability and Multi-Scale Coverability in One and Two Dimensions

Guilhem Gamard 1 Gwenaël Richomme 1, 2
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A word is quasiperiodic (or coverable) if it can be covered with occurrences of another finite word, called its quasiperiod. A word is multi-scale quasiperiodic (or multi-scale coverable) if it has infinitely many different quasiperiods. These notions were previously studied in the domains of text algorithms and combinatorics of right infinite words. We extend them to infinite pictures (two-dimensional words). Then we compare the regularity properties (uniform recurrence, uniform frequencies, topological entropy) of quasiperiodicity with multi-scale quasi-periodicity, and we also compare each of them with its one-dimensional counterpart. We also study which properties of quasiperiods enforce properties on the quasiperiodic words.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01176543
Contributor : Gwenaël Richomme <>
Submitted on : Wednesday, July 15, 2015 - 3:25:58 PM
Last modification on : Thursday, June 6, 2019 - 2:36:38 PM

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  • HAL Id : lirmm-01176543, version 1
  • ARXIV : 1506.08375

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Guilhem Gamard, Gwenaël Richomme. Comparison of Coverability and Multi-Scale Coverability in One and Two Dimensions. 2015. ⟨lirmm-01176543⟩

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