Continued fraction algorithm for Sturmian colorings of trees

Dong Han Kim, Seonhee Lim

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)2541-2569
Number of pages29
JournalErgodic Theory and Dynamical Systems
Volume39
Issue number9
DOIs
StatePublished - 1 Sep 2019

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