Tilings associated with non-Pisot matrices

DOI10.5802/aif.2244zbMath1142.15015OpenAlexW2491407452MaRDI QIDQ2372780

Shunji Ito, E. Arthur jun. Robinson, Maki Furukado

Publication date: 1 August 2007

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2006__56_7_2391_0

zbMATH Keywords

Binet-Cauchy theoremhyperbolic matrixstructure matrixAmmann matrixdeBruijn diagramnon-Pisot conditiontiling substitution

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (4)

Topologically mixing tiling of generated by a generalized substitution ⋮ On the characterization of expansion maps for self-affine tilings ⋮ Geometrical models for a class of reducible Pisot substitutions ⋮ Algebraic numbers, free group automorphisms and substitutions on the plane

Cites Work

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• Canonical substitutions tilings of Ammann-Beenker type
• Tilings from non-Pisot unimodular matrices
• Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms
• Some properties of invertible substitutions of rank \(d\), and higher dimensional substitutions.
• The construction of self-similar tilings
• Nombres algébriques et substitutions
• An Introduction to Symbolic Dynamics and Coding
• Generalized $\beta$-expansions, substitution tilings, and local finiteness
• Pisot substitutions and Rauzy fractals

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