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 quasiperiodicity, 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.
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01176543 Contributor : Gwenaël RichommeConnect in order to contact the contributor Submitted on : Monday, October 25, 2021 - 10:52:01 AM Last modification on : Friday, August 5, 2022 - 3:02:59 PM Long-term archiving on: : Wednesday, January 26, 2022 - 7:06:26 PM
Guilhem Gamard, Gwenaël Richomme. Coverability and multi-scale coverability on infinite pictures. Journal of Computer and System Sciences, Elsevier, 2019, 104, pp.258-277. ⟨10.1016/j.jcss.2017.05.001⟩. ⟨lirmm-01176543⟩