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Quasi-Sturmian colorings on regular trees

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

Aberkane, A.. Words whose complexity satisfies limp (n)/n = 1. Theoret. Comput. Sci. 307(1) (2003), 31–46.Google Scholar
Allouche, J. and Shallit, J.. Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge, 2003.Google Scholar
Cassaigne, J.. Sequences with grouped factors. Developments in Language Theory III (DLT’97). Aristotle University of Thessaloniki, Thessaloniki, 1998, pp. 211–222.Google Scholar
Coven, E.. Sequences with minimal block growth. II. Math. Syst. Theory 8 (1974/75), 376–382.Google Scholar
Kim, D. H. and Lim, S.. Subword complexity and Sturmian colorings of regular trees. Ergod. Th. & Dynam. Sys. 35(2) (2015), 461–481.Google Scholar
Kim, D. H. and Lim, S.. Continued fraction algorithm for Sturmian colorings of trees. Ergod. Th. & Dynam. Sys. (published online in December 2017).Google Scholar
Lothaire, M.. Algebraic Combinatorics on Words (Encyclopedia of Mathematics and its Applications, 90). Cambridge University Press, Cambridge, 2002.Google Scholar
Morse, M. and Hedlund, G.. Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62(1) (1940), 1–42.Google Scholar
Paul, M.. Minimal symbolic flows having minimal block growth. Math. Syst. Theory 8 (1974/75), 309–315.Google Scholar
Pytheas Fogg, N.. Substitutions in Dynamics, Arithmetics and Combinatorics (Lecture Notes in Mathematics, 1794). Springer, Berlin, 2002.Google Scholar
Rauzy, G.. Suites à termes dans un alphabet fini. Séminaire de théorie des nombres de Bordeaux, Exp. No 25, 1982–1983, 1–16.Google Scholar