Hyperbolic tessellation and colorings of trees

Dong Han Kim; Seonhee Lim

doi:10.1155/2013/706496

Hyperbolic tessellation and colorings of trees

Dong Han Kim
, Seonhee Lim

Department of Mathematics Education

Seoul National University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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(H 2), and the element is a commensurator of Γ if and only if its associated coloring is periodic, generalizing a result of Hedlund and Morse.

Original language	English
Article number	706496
Journal	Abstract and Applied Analysis
Volume	2013
DOIs	https://doi.org/10.1155/2013/706496
State	Published - 2013

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AB - 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(H 2), 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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Hyperbolic tessellation and colorings of trees

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