Sturmian colorings of regular trees

In this talk, we study subword complexity $b(n)$ of colorings of regular trees. We classify colorings of subword complexity $b(n) = n + 2$ into periodic colorings, eventually periodic colorings and Sturmian colorings, and study them. We further classify Sturmian colorings of regular trees by their type set. We show that Sturmian colorings are all induced from an innite of bi-innite sequence on a quotient ray of the tree, and that Sturmian colorings of bounded type is induced from an eventually periodic sequence on a quotient ray. This is joint work with Seonhee Lim.