Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Towards a combinatorial algorithm for the enumeration of isotopy classes of tilings on hyperbolic surfaces

Benedikt Kolbe 1
1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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.
Complete list of metadatas

https://hal.inria.fr/hal-03047231
Contributor : Benedikt Kolbe <>
Submitted on : Tuesday, December 8, 2020 - 5:44:31 PM
Last modification on : Thursday, December 10, 2020 - 3:44:59 AM

File

isotopy_algo.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03047231, version 1

Citation

Benedikt Kolbe. Towards a combinatorial algorithm for the enumeration of isotopy classes of tilings on hyperbolic surfaces. 2020. ⟨hal-03047231⟩

Share

Metrics

Record views

33

Files downloads

50