J. Korean Math. Soc. 2015; 52(6): 1123-1137
Printed November 1, 2015
https://doi.org/10.4134/JKMS.2015.52.6.1123
Copyright © The Korean Mathematical Society.
Seul Bee Lee and Seonhee Lim
Seoul National University, Seoul National University
We study colorings of regular trees using subball complexity $b(n)$, which is the number of colored $n$-balls up to color-preserving isomorphisms. We show that for any $k$-regular tree, for $k>1$, there are colorings of intermediate complexity. We then construct colorings of linear complexity $b(n)=2n+2$. We also construct colorings induced from sequences of linear subword complexity which has exponential subball complexity.
Keywords: trees, colorings of trees, subword complexity, symbolic dynamics, Sturmian sequences, Sturmian colorings
MSC numbers: Primary 37B10, 37E25, 05C05
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