# Some algorithms to compute the conjugates of episturmian morphisms

• Volume: 37, Issue: 1, page 85-104
• ISSN: 0988-3754

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## Abstract

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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 $\left\{L,𝔻\right\}$, 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.

## How to cite

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Richomme, Gwenael. "Some algorithms to compute the conjugates of episturmian morphisms." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 37.1 (2003): 85-104. <http://eudml.org/doc/245427>.

@article{Richomme2003,
abstract = {Episturmian morphisms generalize sturmian morphisms. They are defined as compositions of exchange morphisms and two particular morphisms $L$, and $\mathbb \{D\}$. Epistandard morphisms are the morphisms obtained without considering $\mathbb \{D\}$. 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 $\lbrace L, \mathbb \{D\}\rbrace$, 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.},
author = {Richomme, Gwenael},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {combinatorics on words; sturmian morphisms; conjugacy; algorithms; Combinatorics on words; Sturmian morphisms},
language = {eng},
number = {1},
pages = {85-104},
publisher = {EDP-Sciences},
title = {Some algorithms to compute the conjugates of episturmian morphisms},
url = {http://eudml.org/doc/245427},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Richomme, Gwenael
TI - Some algorithms to compute the conjugates of episturmian morphisms
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 1
SP - 85
EP - 104
AB - Episturmian morphisms generalize sturmian morphisms. They are defined as compositions of exchange morphisms and two particular morphisms $L$, and $\mathbb {D}$. Epistandard morphisms are the morphisms obtained without considering $\mathbb {D}$. 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 $\lbrace L, \mathbb {D}\rbrace$, 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.
LA - eng
KW - combinatorics on words; sturmian morphisms; conjugacy; algorithms; Combinatorics on words; Sturmian morphisms
UR - http://eudml.org/doc/245427
ER -

## References

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