| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 428852 | Information Processing Letters | 2015 | 6 Pages |
•We provide a new, short proof of characterization of powers in Sturmian words.•Opposed to previous approaches, we use continued fractions extensively.•Our approach is more geometric and avoids tricky word combinatorial arguments.•We obtain a known formula for the fractional index of Sturmian words as a consequence.
We present a new, dynamical way to study powers (that is, repetitions) in Sturmian words based on results from Diophantine approximation theory. As a result, we provide an alternative and shorter proof of a result by Damanik and Lenz characterizing powers in Sturmian words [6]. Further, as a consequence, we obtain a previously known formula for the fractional index of a Sturmian word based on the continued fraction expansion of its slope.
