Fixed points of Sturmian morphisms and their derivated words
| Autor: | Klouda, Karel, Medková, Kateřina, Pelantová, Edita, Starosta, Štěpán |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Theoretical Computer Science, Volume 743, 2018, Pages 23-37, ISSN 0304-3975 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.tcs.2018.06.037 |
| Popis: | Any infinite uniformly recurrent word ${\bf u}$ can be written as concatenation of a finite number of return words to a chosen prefix $w$ of ${\bf u}$. Ordering of the return words to $w$ in this concatenation is coded by derivated word $d_{\bf u}(w)$. In 1998, Durand proved that a fixed point ${\bf u}$ of a primitive morphism has only finitely many derivated words $d_{\bf u}(w)$ and each derivated word $d_{\bf u}(w)$ is fixed by a primitive morphism as well. In our article we focus on Sturmian words fixed by a primitive morphism. We provide an algorithm which to a given Sturmian morphism $\psi$ lists the morphisms fixing the derivated words of the Sturmian word ${\bf u} = \psi({\bf u})$. We provide a sharp upper bound on length of the list. Comment: 16 pages |
| Databáze: | arXiv |
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