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arXiv · 1609.06064

Continued fraction algorithm for Sturmian colorings of trees

Dong Han Kim·Seonhee Lim
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Abstract

Factor complexity $b_\phi(n)$ for a vertex coloring $\phi$ of a regular tree is the number of colored $n$-balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity $b_\phi(n) = n+2$. In this article, we prove an induction algorithm for Sturmian colorings using colored balls in a way analogous to induction algorithm of Sturmian words. Furthermore, we characterize Sturmian colorings in terms of the data for the induction algorithm.

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Dong Han Kim, Seonhee Lim. 2016-09-20. Continued fraction algorithm for Sturmian colorings of trees. https://doi.org/10.1017/etds.2017.127

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