We consider Sturmian sequences and provide an explicit formula for the index of such a sequence in terms of the continued fraction expansion coefficients of its slope.
Some properties of the factors of Sturmian sequences
โ Scribed by Wei-Ting Cao; Zhi-Ying Wen
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 266 KB
- Volume
- 304
- Category
- Article
- ISSN
- 0304-3975
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๐ SIMILAR VOLUMES
The recurrence quotient is a real number associated to any symbolic sequence. In the case of Sturmian sequences, Morse and Hedlund proved that the smallest possible value is (5 + &)/2. We study here the structure of the set of values taken by the recurrence quotient for a Sturmian sequence.
We show that if a transformation \(T\) on the unit interval is surjective, piecewise continuously differentiable, and uniform distribution preserving, then every u.d. sequence \(\bmod 1\) is the image of some other u.d. sequence \(\bmod 1\) induced by \(T\). As a consequence, we obtain that every u.