Cover Image

A counterexample to the periodic tiling conjecture

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Greenfeld, Rachel, Tao, Terence
Format:	Preprint
Published:	2022
Subjects:	Combinatorics Dynamical Systems 05B45, 52C22, 52C23
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Some variants of the periodic tiling conjecture
by: Greenfeld, Rachel, et al.
Published: (2025)

Periodicity of joint co-tiles in $\mathbb{Z}^d$
by: Meyerovitch, Tom, et al.
Published: (2023)

Undecidable translational tilings with only two tiles, or one nonabelian tile
by: Greenfeld, Rachel, et al.
Published: (2021)

Periodicity and decidability of translational tilings by rational polygonal sets
by: Pont, Jaume de Dios, et al.
Published: (2024)

Colouring monohedral tilings: defects and grain boundaries
by: Alkauskas, Giedrius
Published: (2023)

Self-avoiding space-filling folding curves in dimension 3
by: Oger, Francis
Published: (2025)

Slab tilings, flips and the triple twist
by: Alencar, George L. D., et al.
Published: (2024)

Keller properties for integer tiling
by: Bruce, Benjamin, et al.
Published: (2024)

On the minimal period of integer tilings
by: Łaba, Izabella, et al.
Published: (2024)

How big is a tiling's return module?
by: Perryman, Abigail, et al.
Published: (2024)

Sturmian lattices and Aperiodic tile sets
by: Akiyama, Shigeki, et al.
Published: (2025)

Tiling, spectrality and aperiodicity of connected sets
by: Greenfeld, Rachel, et al.
Published: (2023)

An alternative proof for an aperiodic monotile
by: Akiyama, Shigeki, et al.
Published: (2023)

Overlapping substitutions and tilings
by: Akiyama, Shigeki, et al.
Published: (2024)

The Domino Problem of the Hyperbolic Plane for Regular Polygons
by: Maiti, Arun
Published: (2023)

Turtles, Hats and Spectres: Aperiodic structures on a Rhombic tiling
by: Smith, James
Published: (2024)

Domino tilings of three-dimensional cylinders: regularity of hamiltonian disks
by: de Marreiros, Raphael
Published: (2024)

Fragmenting any Parallelepiped into a Signed Tiling
by: Doolittle, Joseph, et al.
Published: (2023)

3D domino tilings: irregular disks and connected components under flips
by: de Marreiros, Raphael
Published: (2022)

Orbit separation dimension as complexity measure for primitive inflation tilings
by: Baake, Michael, et al.
Published: (2023)

The hat polykite as an Iterated Function System
by: de Wit, Corey
Published: (2025)

An exceptional set of uniformly spread Kakutani tilings of the line
by: Smilansky, Yotam
Published: (2025)

Substitution tilings with transcendental inflation factor
by: Frettlöh, Dirk, et al.
Published: (2022)

Relative Helicity and Tiling Twist
by: Khesin, Boris, et al.
Published: (2024)

The minimum length of an axis-aligned rectangular tiling of a flat torus
by: Lin, Hau-Yi, et al.
Published: (2026)

A characterisation of linear repetitivity for cut and project sets with general polytopal windows
by: Walton, James J.
Published: (2023)

Non-side-to-side tilings of the sphere by congruent triangles with any irrational angle
by: Chen, Wen, et al.
Published: (2025)

Patch frequencies in Penrose rhombic tilings
by: Mazáč, Jan
Published: (2022)

Building with Blocks: Enumerating Polyforms on Tilings
by: Dobbelaere, Bert, et al.
Published: (2026)

Bounds for the collapsibility number of a simplicial complex and non-cover complexes of hypergraphs
by: Santhanam, Rekha, et al.
Published: (2022)

Brillouin Zones of Integer Lattices and Their Perturbations
by: Edelsbrunner, Herbert, et al.
Published: (2022)

Spectral cocycle for substitution tilings
by: Solomyak, Boris, et al.
Published: (2022)

Root polytopes and Jaeger-type dissections for directed graphs
by: Kálmán, Tamás, et al.
Published: (2021)

Bounded remainder sets, bounded distance equivalent cut-and-project sets, and equidecomposability
by: Etkind, Mark Mordechai, et al.
Published: (2025)

Bounded distance equivalence of cut-and-project sets and equidecomposability
by: Grepstad, Sigrid
Published: (2024)

Generalized Integer Partitions, Tilings of Zonotopes and Lattices
by: Latapy, M.
Published: (2000)

Multifractal analysis of measures arising from random substitutions
by: Mitchell, Andrew, et al.
Published: (2023)

A general framework for quasi-isometries in symbolic dynamics beyond groups
by: Barbieri, Sebastián, et al.
Published: (2025)

Integer Area Dissections of Lattice Polygons via a Non-Abelian Sperner's Lemma
by: Abrams, Aaron, et al.
Published: (2024)

Penrose P2 Tilings: A Study of Fully Leafed Induced Subtrees
by: Cloutier, Mathieu, et al.
Published: (2026)