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.
โฆ LIBER โฆ
Limit values of the recurrence quotient of Sturmian sequences
โ Scribed by Julien Cassaigne
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 678 KB
- Volume
- 218
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
โฆ Synopsis
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.
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