Substitution invariant Sturmian words and binary trees

Abstract

We take a global view at substitution invariant Sturmian sequences. We show that homogeneous substitution invariant Sturmian sequences $s_{\alpha ,\alpha }$ can be indexed by two binary trees, associated directly to Johannes Kepler's tree of harmonic fractions from 1619. We obtain similar results for the inhomogeneous sequences $s_{\alpha ,1-\alpha }$ and $s_{\alpha ,0}$.

References in corpus (1)

• Features of a high school olympiad problem

Cited by in corpus (1)

• A remarkable sequence related to $\pi$ and $\sqrt{2}$