Towards a combinatorial algorithm for the enumeration of isotopy classes of tilings on hyperbolic surfaces
| Autor: | Kolbe, Benedikt |
|---|---|
| Přispěvatelé: | Geometric Algorithms and Models Beyond the Linear and Euclidean realm (GAMBLE ), Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), ANR-17-CE40-0033,SoS,Structures sur des surfaces(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Automatic groups
Enumeration Hyperbolic tilings Computational group theory [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS] Orbifolds [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG] Cayley graphs Isotopic tiling theory Delaney-Dress tiling theory Data structure [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] Mapping class groups Coset enumeration Geodesic languages Algorithms |
| Popis: | Based on the mathematical theory of isotopic tilings on hyperbolic surfaces and mapping class groups, we present the, to the best of our knowledge, first algorithms for the enumeration of isotopy classes of tilings by compact disks with a given symmetry group on hyperbolic surfaces, which is moreover combinatorial in nature. This enumeration is relevant for crystallography and materials science. Using the theory of automatic groups, we give some results on the computational tractability of the presented algorithm. We also extend data structures for combinatorial classes of tilings to isotopy classes and give an implementation of the proposed algorithm for certain classes of tilings and illustrate the enumeration with examples. |
| Databáze: | OpenAIRE |
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