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: Dong Han Kim, Seonhee Lim
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/706496
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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.
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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