Continued fraction algorithm for Sturmian colorings of trees

Abstract

Factor complexity $b_{\varphi }(n)$ for a vertex coloring $\varphi$ 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 $b_{\varphi }(n)=n+2$. 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.

32 pages, 3 figure

References in corpus (1)

• Subword complexity and Sturmian colorings of regular trees

Cited by in corpus (1)

• Quasi-Sturmian colorings on regular trees