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Space tilings and local isomorphism
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/j.1538-7305.1961.tb03975.xopenalex-snapshot
Proving Theorems by Pattern Recognition - II
inferredcites →https://doi.org/10.1007/978-94-009-2356-0openalex-snapshot
Computation, logic, philosophy : a collection of essays
inferredcites →https://doi.org/10.1007/978-94-009-2356-0_11openalex-snapshot
Dominoes and the Aea Case of the Decision Problem
inferredcites →https://doi.org/10.1007/bf01020661openalex-snapshot
Correlations in classical ground states
inferredcites →https://doi.org/10.1007/bf02793412openalex-snapshot
Tilings, substitution systems and dynamical systems generated by them
inferredcites →https://doi.org/10.1007/bf03024006openalex-snapshot
Quasicrystals: the view from les houches
inferredcites →https://doi.org/10.1051/jphyscol:1986303openalex-snapshot
WHICH DISTRIBUTIONS OF MATTER DIFFRACT ? AN INITIAL INVESTIGATION
inferredcites →https://doi.org/10.1051/jphyscol:1986305openalex-snapshot
FREQUENCY OF PATTERNS IN CERTAIN GRAPHS AND IN PENROSE TILINGS
inferredcites →https://doi.org/10.1051/jphyscol:1989315openalex-snapshot
WEAKLY PERIODIC STRUCTURES AND EXAMPLE
inferredcites →https://doi.org/10.1090/conm/064/881466openalex-snapshot
Quasicrystals, tilings, and algebraic number theory: some preliminary connections
inferredcites →https://doi.org/10.1090/s0273-0979-1991-16077-5openalex-snapshot
Global order from local sources
inferredcites →https://doi.org/10.1142/s0129055x91000059openalex-snapshot
DISORDERED GROUND STATES OF CLASSICAL LATTICE MODELS
inferredcites →https://doi.org/10.1515/9781400855162openalex-snapshot
Recurrence in Ergodic Theory and Combinatorial Number Theory
inferredcites →https://doi.org/10.4064/fm-82-4-295-305openalex-snapshot
Notes on a class of tiling problems
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Introduction to Hierarchical Tiling Dynamical Systems
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S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry
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Information Compression and Retention in Dynamical Processes
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Diffraction by Aperiodic Structures
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Aperiodic Tilings, Ergodic Theory, and Rotations
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On diffraction by aperiodic structures
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A remark on Schrödinger operators on aperiodic tilings
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The construction of self-similar tilings
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Nonperiodicity implies unique composition for self-similar translationally finite Tilings
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Geometric Models for Quasicrystals II. Local Rules Under Isometries
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Pure Point Dynamical and Diffraction Spectra
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A Characterization of Model Multi-colour Sets
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Circular Symmetry of Pinwheel Diffraction
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Tiling Groupoids and Bratteli Diagrams
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Deformations of simplicial structures
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Conjugacies for Tiling Dynamical Systems
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Minimal Configurations for the Frenkel-Kontorova Model on a Quasicrystal
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Continuity of Eigenfunctions of Uniquely Ergodic Dynamical Systems and Intensity of Bragg Peaks
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Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra
inferred← citeshttps://doi.org/10.1007/s00220-014-2070-5openalex-snapshot
K-Theory of Crossed Products of Tiling C*-Algebras by Rotation Groups
inferred← citeshttps://doi.org/10.1007/s002200000278openalex-snapshot
The Ordered K-Theory of C/*-Algebras¶Associated with Substitution Tilings
inferred← citeshttps://doi.org/10.1007/s002200200594openalex-snapshot
Cohomology of Canonical Projection Tilings
inferred← citeshttps://doi.org/10.1007/s00233-011-9359-xopenalex-snapshot
The tiling C*-algebra viewed as a tight inverse semigroup algebra
inferred← citeshttps://doi.org/10.1007/s00454-001-0033-zopenalex-snapshot
Linear Repetitivity, I. Uniform Subadditive Ergodic Theorems and Applications
inferred← citeshttps://doi.org/10.1007/s00454-002-0758-3openalex-snapshot
Detecting Combinatorial Hierarchy in Tilings Using Derived Voronoi Tessellations
inferred← citeshttps://doi.org/10.1007/s00454-002-2791-7openalex-snapshot
Densest Packing of Equal Spheres in Hyperbolic Space
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On the Characterization of Expansion Maps for Self-Affine Tilings
inferred← citeshttps://doi.org/10.1007/s00605-013-0484-3openalex-snapshot
Metrics on tiling spaces, local isomorphism and an application of Brown’s lemma
inferred← citeshttps://doi.org/10.1007/s10711-020-00560-4openalex-snapshot
Tilings from graph directed iterated function systems
inferred← citeshttps://doi.org/10.1007/s10955-009-9742-0openalex-snapshot
How Model Sets Can Be Determined by Their Two-point and Three-point Correlations
inferred← citeshttps://doi.org/10.1016/j.chaos.2024.114807openalex-snapshot
Tiling iterated function systems
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Brun expansions of stepped surfaces
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Substitution tilings with statistical circular symmetry
inferred← citeshttps://doi.org/10.1016/j.geomphys.2007.07.003openalex-snapshot
Substitution Delone sets with pure point spectrum are inter-model sets
inferred← citeshttps://doi.org/10.1016/j.geomphys.2007.12.006openalex-snapshot
Dworkin’s argument revisited: Point processes, dynamics, diffraction, and correlations
inferred← citeshttps://doi.org/10.1016/j.geomphys.2016.11.010openalex-snapshot
Fractal spectral triples on Kellendonk’s C∗ -algebra of a substitution tiling
inferred← citeshttps://doi.org/10.1016/j.geomphys.2021.104217openalex-snapshot
Relating diffraction and spectral data of aperiodic tilings: Towards a Bloch theorem
inferred← citeshttps://doi.org/10.1016/j.jcta.2018.07.002openalex-snapshot
Lots of aperiodic sets of tiles
inferred← citeshttps://doi.org/10.1016/j.jmaa.2007.02.040openalex-snapshot
The properties of a family of tiles with a parameter
inferred← citeshttps://doi.org/10.1016/j.tcs.2004.02.019openalex-snapshot
Algebraic and model-theoretic properties of tilings
inferred← citeshttps://doi.org/10.1016/j.topol.2004.08.014openalex-snapshot
Multidimensional constant-length substitution sequences
inferred← citeshttps://doi.org/10.1016/s0921-5093(00)01193-xopenalex-snapshot
The impact of aperiodic order on mathematics
inferred← citeshttps://doi.org/10.1017/etds.2013.27openalex-snapshot
Second-order ergodic theorem for self-similar tiling systems
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Stationary processes and pure point diffraction
inferred← citeshttps://doi.org/10.1017/s0143385701001572openalex-snapshot
Isomorphism of hierarchical structures
inferred← citeshttps://doi.org/10.1017/s0143385702001566openalex-snapshot
Repetitive Delone sets and quasicrystals
inferred← citeshttps://doi.org/10.1017/s0143385710000064openalex-snapshot
An example of a non-uniquely ergodic lamination
inferred← citeshttps://doi.org/10.1017/s0143385710000696openalex-snapshot
Rigidity and mapping class group for abstract tiling spaces
inferred← citeshttps://doi.org/10.1017/s0143385797084988openalex-snapshot
Dynamics of self-similar tilings
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An Algebraic Invariant for Substitution Tiling Systems
inferred← citeshttps://doi.org/10.1023/a:1005191014127openalex-snapshot
Towards a Characterization of Self-Similar Tilings in Terms of Derived Voronoï Tessellations
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A Homeomorphism Invariant for Substitution Tiling Spaces
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On the Existence of Completely Saturated Packings and Completely Reduced Coverings
inferred← citeshttps://doi.org/10.1023/b:geom.0000006580.47816.e9openalex-snapshot
Periodicity and Circle Packings of the Hyperbolic Plane
inferred← citeshttps://doi.org/10.1023/b:geom.0000022857.62695.15openalex-snapshot
Optimally Dense Packings of Hyperbolic Space
inferred← citeshttps://doi.org/10.1063/1.1521239openalex-snapshot
Kolakoski-(2m,2n) are limit-periodic model sets
inferred← citeshttps://doi.org/10.1080/14786430801908062openalex-snapshot
About substitution tilings with statistical circular symmetry
inferred← citeshttps://doi.org/10.1080/14786430802082008openalex-snapshot
Aperiodic order and pure point diffraction
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Quasicrystals and Denjoy homeomorphisms
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Equivalence between pure point diffractive sets and cut-and-project sets on substitution tilings
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The characterization of ground states
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Electrons in deterministic quasicrystalline potentials and hidden conserved quantities
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Aperiodic order via dynamical systems: diffraction for sets of finite local complexity
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Spectrum of dynamical systems arising from Delone sets
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Topological invariants for projection method patterns
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Aperiodic Tilings in Higher Dimensions
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The dynamical properties of Penrose tilings
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Symmetry of tilings of the plane
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Self-similarity and spectral theory: on the spectrum of substitutions
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Computing with almost periodic functions
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Pure discrete spectrum and regular model sets in d-dimensional unimodular substitution tilings
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Mathematical quasicrystals: a tale of two topologies
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Tiling Spaces of Taylor-Socolar Tilings
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Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximations in 1D
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Recent developments in the mathematics of diffraction
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Actions of Finite Groups on Substitution Tilings and Their Associated C*-algebras
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Eigenfunctions for substitution tiling systems
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On orbit closure decompositions of tiling spaces by the generalized projection method
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Remarks on 2-dimensional quasiperiodic tilings with rotational symmetries
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Cut-and-Project Schemes for Pisot Family Substitution Tilings
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On the Notions of Symmetry and Aperiodicity for Delone Sets
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Statistical stability for multi-substitution tiling spaces
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Dynamical properties of almost repetitive Delone sets
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On substitution tilings and Delone sets without finite local complexity
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An application of topological multiple recurrence to tiling
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Percolation on Penrose Tilings
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Local Complexity of Delone Sets and Crystallinity
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Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type
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Point Sets and Dynamical Systems In the Autocorrelation Topology
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Discrete Sets and Associated Dynamical Systems in a Non-Commutative Setting
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Self-similarity and limit spaces of substitution tiling semigroups
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Structural aspects of tilings
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Random colourings of aperiodic graphs: Ergodic and spectral properties
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Dynamique transverse de la lamination de Ghys-Kenyon
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The Jewett-Krieger Construction for Tilings
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C*-algebras of tilings with infinite rotational symmetry
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Stationary processes with pure point diffraction
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$\boldsymbol{S}$-adic sequences. A bridge between dynamics, arithmetic, and geometry
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Tiling Iterated Function Systems
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Cohomology groups for projection point patterns
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Isomorphism of Hierarchical Structures
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Topological invariants for projection method patterns
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On the existence of completely saturated packings and completely reduced covering
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Uniqueness and Symmetry in Problems of Optimally Dense Packings
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The Construction of Self-Similar Tilings
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On a generalization of the Selection Theorem of Mahler
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K-théorie pour les C*-algèbres de pavages de Penrose hyperboliques
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