| Autor: |
Dolce, Francesco, Dvorakova, Lubomira, Pelantova, Edita |
| Rok vydání: |
2021 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.tcs.2022.10.014 |
| Popis: |
We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We show that the language of v is eventually dendric and we focus on return words to its factors. We develop a method for computing the critical exponent and asymptotic critical exponent of balanced sequences, provided the associated Sturmian sequence u has a quadratic slope. The method is based on looking for the shortest return words to bispecial factors in v. We illustrate our method on several examples; in particular we confirm a conjecture of Rampersad, Shallit and Vandomme that two specific sequences have the least critical exponent among all balanced sequences over 9-letter (resp., $0-letter) alphabets. |
| Databáze: |
arXiv |
| Externí odkaz: |
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