Nonexpansive $\mathbb {Z}^2$-subdynamics and Nivat’s Conjecture

DOI10.1090/S0002-9947-2015-06391-0zbMath1353.37035arXiv1208.4090WikidataQ123290734 ScholiaQ123290734MaRDI QIDQ5264929

Van Cyr, Bryna Kra

Publication date: 20 July 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.4090

zbMATH Keywords

periodicityNivat's conjectureblock complexitynonexpansive subdynamics\(\mathbb{Z}^2\)-subshift

Mathematics Subject Classification ID

Combinatorics on words (68R15) Symbolic dynamics (37B10)

Related Items (25)

The spacetime of a shift endomorphism ⋮ Tree shift topological entropy ⋮ An Algebraic Geometric Approach to Multidimensional Words ⋮ Free ergodic ℤ²-systems and complexity ⋮ Homomorphisms between multidimensional constant-shape substitutions ⋮ Expansivity and periodicity in algebraic subshifts ⋮ On periodic decompositions, one-sided nonexpansive directions and Nivat's conjecture ⋮ Balancedness and coboundaries in symbolic systems ⋮ Nivat's conjecture and pattern complexity in algebraic subshifts ⋮ Complexity of short rectangles and periodicity ⋮ Rapid left expansivity, a commonality between Wolfram's rule 30 and powers of \(p/q\) ⋮ Minimal Complexities for Infinite Words Written with d Letters ⋮ On periodic decompositions and nonexpansive lines ⋮ Nonexpansive directions in the Jeandel-Rao Wang shift ⋮ An alphabetical approach to Nivat’s conjecture ⋮ Decidability and periodicity of low complexity tilings ⋮ Distortion and the automorphism group of a shift ⋮ Bounded complexity, mean equicontinuity and discrete spectrum ⋮ Automaticity and Invariant Measures of Linear Cellular Automata ⋮ Complexity and directional entropy in two dimensions ⋮ Cutting corners ⋮ An algebraic geometric approach to Nivat's conjecture ⋮ Aperiodic two-dimensional words of small abelian complexity ⋮ Recurrence along directions in multidimensional words ⋮ Domino problem for pretty low complexity subshifts

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