Abstract
Let S be a standard Sturmian word that is a fixed point of a non-trivial homomorphism. Associated to the infinite word S is a unique irrational number β with 0 <β <1. We prove that the standard Sturmian word S contains no fractional power with exponent greater than Ω and that for any real number ε > 0 it contains a fractional power with exponent greater than Ω - ε; here Ω is a constant that depends on β. The constant Ω is given explicitly. Using these results we are able to give a short proof of Mignosi's theorem and give an exact evaluation of the maximal power that can occur in a standard Sturmian word.
Original language | English |
---|---|
Pages (from-to) | 283-300 |
Number of pages | 18 |
Journal | Theoretical Computer Science |
Volume | 242 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2000 |
Keywords
- Critical exponent
- Lyndon-schutzenberger theorem
- Sturmian words