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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 706496, 6 pages
http://dx.doi.org/10.1155/2013/706496
Research Article

Hyperbolic Tessellation and Colorings of Trees

1Department of Mathematics Education, Dongguk University-Seoul, Seoul 100-715, Republic of Korea
2Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea

Received 22 February 2013; Accepted 3 May 2013

Academic Editor: Baodong Zheng

Copyright © 2013 Dong Han Kim and Seonhee Lim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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( ), and the element is a commensurator of if and only if its associated coloring is periodic, generalizing a result of Hedlund and Morse.