Fixed points of Sturmian morphisms and their derivated words
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1801.09203
 Bibcode:
 2018arXiv180109203K
 Keywords:

 Mathematics  Combinatorics;
 68R15
 EPrint:
 16 pages