2018/12/19 by Guilhem Gamard, Gamard, Guilhem
Computer Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1812.08022
openalex publication_date 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A coloration w of Z2 is said to be coverable if there exists a rectangular block q such that w is covered with occurrences of q, possibly overlapping. In this case, q is a cover of w. A subshift is said to have the cover q if each of its points has the cover q. In a previous article, we characterized the covers that force subshifts to be finite (in particular, all configurations are periodic). We also noticed that some covers force subshifts to have zero topological entropy while not forcing them to be finite. In the current paper we work towards characterizing precisely covers which force a subshift to have zero entropy, but not necessarily periodicity. We give a necessary condition and a sufficient condition which are close, but not quite identical.