کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
428852 | 686943 | 2015 | 6 صفحه PDF | دانلود رایگان |
• 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.
Journal: Information Processing Letters - Volume 115, Issue 11, November 2015, Pages 886–891