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Continued fraction algorithm for Sturmian colorings of trees
- Authors
- Kim, Dong Han; Lim, Seonhee
- Issue Date
- Sep-2019
- Publisher
- CAMBRIDGE UNIV PRESS
- Citation
- ERGODIC THEORY AND DYNAMICAL SYSTEMS, v.39, no.9, pp 2541 - 2569
- Pages
- 29
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- ERGODIC THEORY AND DYNAMICAL SYSTEMS
- Volume
- 39
- Number
- 9
- Start Page
- 2541
- End Page
- 2569
- ISSN
- 0143-3857
1469-4417
- Abstract
- Factor complexity b(n) (phi) for a vertex coloring phi of a regular tree is the number of classes of n-balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity b(n) (phi) = n + 2. In this article, we prove an induction algorithm for Sturmian colorings using colored balls in a way analogous to the continued fraction algorithm for Sturmian words. Furthermore, we characterize Sturmian colorings in terms of the data appearing in the induction algorithm.
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Related Researcher
- Kim, Dong Han
- College of Education (Department of Mathematics Education)