A characterization of Sturmian sequences by indistinguishable asymptotic pairs

Complete Characterization of Substitution Invariant Sturmian Sequences

We provide a complete characterization of substitution invariant inhomogeneous bidirectional pointed Sturmian sequences. The result is analogous to that obtained by Berthé et al. [5] and Yasutomi [21] for one-directional Sturmian words. The proof is constructive, based on the geometric representation of Sturmian words by a cut-and-project scheme.

Powers in Sturmian sequences

A Characterization of Sturmian Morphisms

A one-sided infinite word is balanced if the difference of the number of occurrences of a letter in two factors of the same length never exceeds one. It is Sturmian if it is balanced and not ultimately periodic. Sturmian words have a long history. A clear exposition of early work by J. Bernoulli, Christoffel, and A. A. Markov is given in the book by Venkov [22]. The term "Sturmian" has been use...

Initial Powers of Sturmian Sequences

We investigate powers of prefixes in Sturmian sequences. We obtain an explicit formula for ice(ω), the initial critical exponent of a Sturmian sequence ω, defined as the supremum of all real numbers p > 0 for which there exist arbitrary long prefixes of ω of the form u, in terms of its S-adic representation. This formula is based on Ostrowski’s numeration system. We characterize those irrationa...

The Index of Sturmian Sequences