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Ergodic Theory and Dynamical Systems Ergodic Theory and Dynamical Systems

Article contents

Quasi-Sturmian colorings on regular trees

Part of: Graph theory Special aspects of infinite or finite groups Discrete mathematics in relation to computer science Low-dimensional dynamical systems Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 August 2019

DONG HAN KIM ,
SEUL BEE LEE ,
SEONHEE LIM  and
DEOKWON SIM
DONG HAN KIM
Affiliation:
Department of Mathematics Education, Dongguk University–Seoul, 30 Pildong-ro 1-gil, Junggu, Seoul04620, Korea email kim2010@dongguk.edu
SEUL BEE LEE
Affiliation:
Department of Mathematical Sciences, Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul08826, Korea email seulbee.lee@snu.ac.kr, deokwon.sim@snu.ac.kr
SEONHEE LIM
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul08826, Korea email seonhee.lim@gmail.com
DEOKWON SIM
Affiliation:
Department of Mathematical Sciences, Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul08826, Korea email seulbee.lee@snu.ac.kr, deokwon.sim@snu.ac.kr
Corresponding
E-mail address:
kim2010@dongguk.edu
seulbee.lee@snu.ac.kr
deokwon.sim@snu.ac.kr
seonhee.lim@gmail.com
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Abstract

Quasi-Sturmian words, which are infinite words with factor complexity eventually $n+c$ share many properties with Sturmian words. In this article, we study the quasi-Sturmian colorings on regular trees. There are two different types, bounded and unbounded, of quasi-Sturmian colorings. We obtain an induction algorithm similar to Sturmian colorings. We distinguish them by the recurrence function.

Keywords

symbolic dynamics arithmetic and algebraic dynamics group actions

MSC classification

Primary: 20E08: Groups acting on trees
Secondary: 20F65: Geometric group theory 05C15: Coloring of graphs and hypergraphs 37E25: Maps of trees and graphs 68R15: Combinatorics on words
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 12 , December 2020 , pp. 3403 - 3419
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Copyright
© Cambridge University Press, 2019

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References

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