Sturmian coloring or regular trees

In this talk, we introduce subword complexity of colorings of regular trees. We characterize colorings of bounded subword complexity and then introduce Sturmian colorings, which are colorings of minimal unbounded subword complexity. We classify Sturmian colorings using their type sets. We show that any Sturmian coloring is a lifting of a coloring on a quotient graph of the tree which is a geodesic or a ray, with loops possibly attached, thus a lifting of an "infinte word". We further give a complete characterization of the quotient graph for eventually periodic ones. We will provide several examples. This is joint work with Seonhee Lim.

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