# Some algorithms to compute the conjugates of Episturmian morphisms

RAIRO - Theoretical Informatics and Applications (2010)

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

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topRichomme, Gwenael. "Some algorithms to compute the conjugates of Episturmian morphisms." RAIRO - Theoretical Informatics and Applications 37.1 (2010): 85-104. <http://eudml.org/doc/92715>.

@article{Richomme2010,

abstract = {
Episturmian morphisms generalize Sturmian morphisms. They are defined
as compositions of exchange morphisms and two particular morphisms
L, and R. Epistandard morphisms are the morphisms obtained without
considering R. 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,R\},
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},

keywords = {Combinatorics on words; Sturmian morphisms; conjugacy;
algorithms.; algorithms},

language = {eng},

month = {3},

number = {1},

pages = {85-104},

publisher = {EDP Sciences},

title = {Some algorithms to compute the conjugates of Episturmian morphisms},

url = {http://eudml.org/doc/92715},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Richomme, Gwenael

TI - Some algorithms to compute the conjugates of Episturmian morphisms

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

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 R. Epistandard morphisms are the morphisms obtained without
considering R. 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,R},
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.; algorithms

UR - http://eudml.org/doc/92715

ER -

## References

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