On entropies of block-gluing subshifts

2020/12/17 by Svetlana Puzynina, Mathieu Sablik, Puzynina, Svetlana +1
Computer Science · Mathematics · #03D78 #37B40 #68R15 #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #F.1.1 #FOS: Computer and information sciences #G.2.1 #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2012.09415

openalex publication_date 2020/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A subshift X is called c-block gluing if for any integer n≥ c and any two blocks u and v from the language of X there exists an element of X which has occurrences of u and v at distance n. In this note we study the topological entropies of c-block gluing binary one-dimensional subshifts. We define the set R_c to be the set of entropies of all c-block-gluing subshifts, and R=∪_{c∈ ℕ} R_c. We show that the set R is dense, while R₁ and R₂ are not; in particular, they have isolated points. We conjecture that the same holds for any c.

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