Abstract
Factor complexity for a vertex coloring of a regular tree is the number of classes of -balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity . 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.
Original language | English |
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Pages (from-to) | 2541-2569 |
Number of pages | 29 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 39 |
Issue number | 9 |
DOIs | |
State | Published - 1 Sep 2019 |