We study the action of right conjugates of a standard morphism on the infinite word (if it exists)
generated by this morphism. When $g$ is the $i$-th right conjugate of a standard morphism generating an infinite word
${\bf x}$, $g({\bf x})$ is the $i$-th conjugate of ${\bf x}$. We design an algorithm to obtain a canonical decomposition of all the
right conjugates of a standard morphism. As an application we compute the sequence of conjugates of the powers of the
Fibonacci morphism and then we generalize, to all the conjugates of ${\bf F}$, Wen and Wen's decomposition of the Fibonacci
word ${\bf F}$ in singular words.
Publié le : 2003-12-14
Classification:
Sturmian words and morphisms,
standard morphisms,
conjugates,
Fibonacci word and morphism,
singular words,
68R15
@article{1074791329,
author = {Lev\'e, Florence and S\'e\'ebold, Patrice},
title = {Conjugation of standard morphisms and a generalization of singular words},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {10},
number = {1},
year = {2003},
pages = { 737-747},
language = {en},
url = {http://dml.mathdoc.fr/item/1074791329}
}
Levé, Florence; Séébold, Patrice. Conjugation of standard morphisms and a generalization of singular words. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp. 737-747. http://gdmltest.u-ga.fr/item/1074791329/