Hyperbolic Tessellation and Colorings of Trees
We study colorings of a tree induced from isometries of the hyperbolic plane given an ideal tessellation. We show that, for a given tessellation of the hyperbolic plane by ideal polygons, a coloring can be associated with any element of Isom(ℍ2), and the element is a commensurator of Γ if and only i...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/706496 |
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| _version_ | 1850172265137700864 |
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| author | Dong Han Kim Seonhee Lim |
| author_facet | Dong Han Kim Seonhee Lim |
| author_sort | Dong Han Kim |
| collection | DOAJ |
| description | We study colorings of a tree induced from
isometries of the hyperbolic plane given an ideal tessellation. We
show that, for a given tessellation of the hyperbolic plane by
ideal polygons, a coloring can be associated with any element of
Isom(ℍ2), and the element is a commensurator of Γ
if and only if its associated coloring is periodic, generalizing a result of Hedlund and Morse. |
| format | Article |
| id | doaj-art-cfd5084e1a5746f29c1209fb4619c20e |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cfd5084e1a5746f29c1209fb4619c20e2025-08-20T02:20:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/706496706496Hyperbolic Tessellation and Colorings of TreesDong Han Kim0Seonhee Lim1Department of Mathematics Education, Dongguk University-Seoul, Seoul 100-715, Republic of KoreaDepartment of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of KoreaWe study colorings of a tree induced from isometries of the hyperbolic plane given an ideal tessellation. We show that, for a given tessellation of the hyperbolic plane by ideal polygons, a coloring can be associated with any element of Isom(ℍ2), and the element is a commensurator of Γ if and only if its associated coloring is periodic, generalizing a result of Hedlund and Morse.http://dx.doi.org/10.1155/2013/706496 |
| spellingShingle | Dong Han Kim Seonhee Lim Hyperbolic Tessellation and Colorings of Trees Abstract and Applied Analysis |
| title | Hyperbolic Tessellation and Colorings of Trees |
| title_full | Hyperbolic Tessellation and Colorings of Trees |
| title_fullStr | Hyperbolic Tessellation and Colorings of Trees |
| title_full_unstemmed | Hyperbolic Tessellation and Colorings of Trees |
| title_short | Hyperbolic Tessellation and Colorings of Trees |
| title_sort | hyperbolic tessellation and colorings of trees |
| url | http://dx.doi.org/10.1155/2013/706496 |
| work_keys_str_mv | AT donghankim hyperbolictessellationandcoloringsoftrees AT seonheelim hyperbolictessellationandcoloringsoftrees |