The Domino Problem of the Hyperbolic Plane for Regular Polygons
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911551573721088 |
|---|---|
| author | Maiti, Arun |
| author_facet | Maiti, Arun |
| contents | We provide a definitive classification of all finite sets of regular polygons that admit a tiling of the hyperbolic plane, thereby establishing the decidability of the Domino Problem for this class of prototiles. We show that admissibility is determined by a finite set of local and inductive combinatorial constraints. This classification further leads to the discovery of the first known examples of weakly aperiodic protosets consisting of regular polygons in $\mathbb{H}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05661 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Domino Problem of the Hyperbolic Plane for Regular Polygons Maiti, Arun Combinatorics Geometric Topology 05B45, 52C20, 52C23 We provide a definitive classification of all finite sets of regular polygons that admit a tiling of the hyperbolic plane, thereby establishing the decidability of the Domino Problem for this class of prototiles. We show that admissibility is determined by a finite set of local and inductive combinatorial constraints. This classification further leads to the discovery of the first known examples of weakly aperiodic protosets consisting of regular polygons in $\mathbb{H}^2$. |
| title | The Domino Problem of the Hyperbolic Plane for Regular Polygons |
| topic | Combinatorics Geometric Topology 05B45, 52C20, 52C23 |
| url | https://arxiv.org/abs/2302.05661 |