Geometric Models for Quasicrystals I. Delone Sets of Finite Type

Jeffrey C. Lagarias

Type: Article

Publication Date: 1999-02-01

Citations: 131

DOI: https://doi.org/10.1007/pl00009413

View Publication

Download PDF

Locations

Discrete & Computational Geometry - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Geometric Models for Quasicrystals II. Local Rules Under Isometries	1999	Jeffrey C. Lagarias
+ PDF Chat	Repetitive Delone sets and quasicrystals	2003	Jeffrey C. Lagarias P. A. B. Pleasants
+	Model sets with predefined local structure	2004	Nicolae Cotfas
+ PDF Chat	Some examples of repetitive, nonrectifiable Delone sets	2016	María Isabel Cortéz Andrés Navas
+	Local Complexity of Delone Sets and Crystallinity	2001	J. C. Lagarias P. A. B. Pleasants
+	Repetitive Delone Sets and Quasicrystals	1999	J. C. Lagarias P. A. B. Pleasants
+	Local groups in Delone sets in the Euclidean space	2022	Nikolay Dolbilin Михаил Иванович Штогрин
+	Almost finiteness of groupoid actions and Z-stability of C*-algebras associated to tilings	2019	Luke John Ito
+ PDF Chat	Local Complexity of Delone Sets and Crystallinity	2002	Jeffrey C. Lagarias P. A. B. Pleasants
+ PDF Chat	Multiregular Point Systems	1998	Н. П. Долбилин Jeffrey C. Lagarias Marjorie Senechal
+	A guide to mathematical quasicrystals	1999	Michael Baake
+	Random Tiling Models for Quasicrystals	2000	Eric Cockayne
+	Local rules for multi-dimensional quasicrystals	1995	Le Tu Quoc Thang Sergey Piunikhin
+	On generalized self-similarities of cut-and-project sets	2019	Zuzana Masáková Jan Mazáč Edita Pelantová
+	On generalized self-similarities of cut-and-project sets	2019	Zuzana Masáková Jan Mazáč Edita Pelantová
+	Quasicrystals	2019	Uwe Grimm Peter Krämer
+ PDF Chat	On rectifiability of Delone sets in intermediate regularity	2024	Irene Inoquio-Renteria Rodolfo Viera
+ PDF Chat	Aperiodic crystals and beyond	2014	Uwe Grimm Michael Baake
+	Matching Rules for Quasicrystalline Tilings	1999	Kevin Ingersent
+	Matching Rules for Quasicrystalline Tilings	1991	Kevin Ingersent

Works That Cite This (101)

Action	Title	Year	Authors
+ PDF Chat	Local versions of the Wiener–Lévy theorem	2022	S. Favorov
+	Spectral approximation of aperiodic Schr\"odinger operators	2016	Siegfried Beckus
+ PDF Chat	The characterization of ground states	2010	Jean Bellissard Charles Radin Senya Shlosman
+	Quasicrystals: algebraic, combinatorial and geometrical aspects	2006	Edita Pelantová Zuzana Masáková
+ PDF Chat	A spectral sequence for the<i>K</i>-theory of tiling spaces	2009	Jean Savinien Jean Bellissard
+ PDF Chat	A classification of aperiodic order via spectral metrics and Jarník sets	2018	Maik Gröger Marc Keßeböhmer A. Mosbach Tony Samuel M. Steffens
+	Algorithm for determining pure pointedness of self-affine tilings	2010	Shigeki Akiyama Jeong-Yup Lee
+ PDF Chat	Diffusion on Delone sets	2017	Sebastian Haeseler Xueping Huang Daniel Lenz Felix Pogorzelski
+ PDF Chat	Multiregular Point Systems	1998	Н. П. Долбилин Jeffrey C. Lagarias Marjorie Senechal
+ PDF Chat	On the Characterization of Expansion Maps for Self-Affine Tilings	2009	Richard Kenyon Boris Solomyak

Works Cited by This (28)

Action	Title	Year	Authors
+	On periodic and non-periodic space fillings of Em obtained by projection	2005	Peter Krämer Rebecca Colina Neri
+	An Introduction to Symbolic Dynamics and Coding	2010	Douglas Lind Brian Marcus
+	Quasiperiodicity: Local and global aspects	2008	Ludwig Danzer
+	Pisot and Salem Numbers	1992	Marie José Bertin A. Decomps-Guilloux M. Grandet-Hugot M. Pathiaux-Delefosse J. P. Schreiber
+	Tilings and Patterns.	1988	Solomon W. Golomb Branko Grünbaum G. C. Shephard
+ PDF Chat	Nonperiodicity implies unique composition for self-similar translationally finite Tilings	1998	Boris Solomyak
+	Matrices of Perron numbers	1992	Douglas Lind
+	Spectrum of dynamical systems arising from Delone sets	1998	Boris Solomyak
+	On a “structure intermediate between quasiperiodic and random”	1996	At L. Hof
+ PDF Chat	The construction of self-similar tilings	1996	Richard Kenyon