Atomic surfaces, tilings and coincidence. I: Irreducible case

DOI10.1007/BF02771781zbMath1143.37013OpenAlexW3204164517MaRDI QIDQ2480555

Hui Rao, Shunji Ito

Publication date: 1 April 2008

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02771781

zbMATH Keywords

quasiperiodicitytilingsatomic surfacecoicidence conditionirreducible Pisot substitution

Mathematics Subject Classification ID

Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (37)

Purely periodic 𝛽-expansions with Pisot unit base ⋮ Dynamical directions in numeration ⋮ Fractal representation of the attractive lamination of an automorphism of the free group. ⋮ Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to \(\beta\)-shifts ⋮ Atomic surfaces, tilings and coincidences. II: Reducible case ⋮ Substitutions, abstract number systems and the space filling property ⋮ Strong coincidence and overlap coincidence ⋮ Unimodular Pisot substitutions and their associated tiles ⋮ Discrepancy Bounds for β $$\boldsymbol{\beta }$$ -adic Halton Sequences ⋮ Fractal tiles associated with shift radix systems ⋮ Rational self-affine tiles ⋮ Decidability Problems for Self-induced Systems Generated by a Substitution ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ Natural extensions for piecewise affine maps via Hofbauer towers ⋮ Geometry, dynamics, and arithmetic of $S$-adic shifts ⋮ Convex polyhedra with deltoidal vertices ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ Stepped surfaces and Rauzy fractals induced from automorphisms on the free group of rank 2 ⋮ Dual systems of algebraic iterated function systems ⋮ Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings ⋮ Study of irreducible balanced pairs for substitutive languages ⋮ S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry ⋮ Yet Another Characterization of the Pisot Substitution Conjecture ⋮ Beta-expansions, natural extensions and multiple tilings associated with Pisot units ⋮ The geometry of non-unit Pisot substitutions ⋮ Multiple tilings associated to \(d\)-Bonacci beta-expansions ⋮ Purely periodic \(\beta \)-expansions in the Pisot non-unit case ⋮ Geometrical models for a class of reducible Pisot substitutions ⋮ Tilings for Pisot beta numeration ⋮ Homological Pisot substitutions and exact regularity ⋮ On substitution invariant Sturmian words: an application of Rauzy fractals ⋮ Periodic codings of algebraic graph-directed IFS ⋮ Non-Unimodularity ⋮ Topological properties of a class of cubic Rauzy fractals ⋮ On self-affine tiles whose boundary is a sphere ⋮ \(AH\)-substitution and Markov partition of a group automorphism on \(T^d\) ⋮ A combinatorial approach to products of Pisot substitutions

Cites Work

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