Semi-strongly irreducible shifts
type: Item
instance of: scholarly article
title: Semi-strongly irreducible shifts
zbMATH Open document ID: 1058.37009
DOI: 10.1016/S0196-8858(03)00053-8
author: Francesca Fiorenzi
published in: Advances in Applied Mathematics
publication date: 2004-10-12T00:00:00Z
review text: This paper continues the author's study of local functions on subshifts. In earlier work [PU.M.A., Pure Math. Appl. 11, 471--484 (2000; Zbl 0980.37004)] the author showed the equivalence of pre-injectivity and surjectivity for irreducible shifts of finite type, then in [Theor. Comput. Sci. 299, 477--493 (2003; Zbl 1042.68077)] she defined a notion of strong irreducibility which together with a finite type condition ensures the same property for such shifts in \(A^{\Gamma}\), where \(\Gamma\) is an amenable group. Here, the work is taken in a slightly different direction, with the introduction of a property called semi-strong irreducibility, with the result that pre-injectivity implies surjectivity for a local function on a semi-strongly irreducible shift of finite type in \(A^{\Gamma}\) for any group \(\Gamma\) of non-exponential growth. An interesting byproduct is a proof that proper subshifts of such shifts have strictly smaller entropy.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 37B15
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 68Q80
Mathematics Subject Classification ID: 37B10
zbMATH DE Number: 2107246
zbMATH Keywords: irreducible shifts
zbMATH Keywords: amenable groups
zbMATH Keywords: entropy
zbMATH Keywords: subshift
MaRDI profile type: Publication
cites work: Topological Entropy
cites work: Amenable groups and cellular automata
cites work: Q5821603
cites work: The Garden of Eden theorem for sofic shifts
cites work: Cellular automata and strongly irreducible shifts of finite type.
cites work: On groups with full Banach mean value
cites work: Q5562332
cites work: Endomorphisms of symbolic algebraic varieties
cites work: An Introduction to Symbolic Dynamics and Coding
cites work: Q5333602
cites work: Garden of Eden Configurations for Cellular Automata on Cayley Graphs of Groups
cites work: A note on curvature and fundamental group
cites work: Shorter Note: The Converse of Moore's Garden-of-Eden Theorem
cites work: Folner's Conditions for Amenable Semi-Groups.
cites work: Tesselations with local transformations
cites work: A Mathematical Theory of Communication
cites work: Q3226242
cites work: Q5815903
full work available at URL: s0196-8858(03)00053-8
OpenAlex ID: W2093672868
description: scientific article; zbMATH DE number 2107246