Some algorithms to compute the conjugates of episturmian morphisms

Richomme, Gwenael

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 1, pp. 85-104.

Episturmian morphisms generalize sturmian morphisms. They are defined as compositions of exchange morphisms and two particular morphisms $L$, and $𝔻$. Epistandard morphisms are the morphisms obtained without considering $𝔻$. In [14], a general study of these morphims and of conjugacy of morphisms is given. Here, given a decomposition of an Episturmian morphism $f$ over exchange morphisms and $\{L,𝔻\}$, we consider two problems: how to compute a decomposition of one conjugate of $f$; how to compute a list of decompositions of all the conjugates of $f$ when $f$ is epistandard. For each problem, we give several algorithms. Although the proposed methods are fundamently different, we show that some of these lead to the same result. We also give other algorithms, using the same input, to compute for instance the length of the morphism, or its number of conjugates.

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