# Morphisms preserving the set of words coding three interval exchange∗∗∗

RAIRO - Theoretical Informatics and Applications (2012)

- Volume: 46, Issue: 1, page 107-122
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topHejda, Tomáš. "Morphisms preserving the set of words coding three interval exchange∗∗∗." RAIRO - Theoretical Informatics and Applications 46.1 (2012): 107-122. <http://eudml.org/doc/221983>.

@article{Hejda2012,

abstract = {Any amicable pair ϕ, ψ of Sturmian morphisms enables a
construction of a ternary morphism η which preserves the set of infinite
words coding 3-interval exchange. We determine the number of amicable pairs with the same
incidence matrix in SL±(2,ℕ) and we study incidence matrices
associated with the corresponding ternary morphisms η.},

author = {Hejda, Tomáš},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Interval exchange; three interval exchange; amicable Sturmian morphisms; incidence matrix of morphism; interval exchange},

language = {eng},

month = {3},

number = {1},

pages = {107-122},

publisher = {EDP Sciences},

title = {Morphisms preserving the set of words coding three interval exchange∗∗∗},

url = {http://eudml.org/doc/221983},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Hejda, Tomáš

TI - Morphisms preserving the set of words coding three interval exchange∗∗∗

JO - RAIRO - Theoretical Informatics and Applications

DA - 2012/3//

PB - EDP Sciences

VL - 46

IS - 1

SP - 107

EP - 122

AB - Any amicable pair ϕ, ψ of Sturmian morphisms enables a
construction of a ternary morphism η which preserves the set of infinite
words coding 3-interval exchange. We determine the number of amicable pairs with the same
incidence matrix in SL±(2,ℕ) and we study incidence matrices
associated with the corresponding ternary morphisms η.

LA - eng

KW - Interval exchange; three interval exchange; amicable Sturmian morphisms; incidence matrix of morphism; interval exchange

UR - http://eudml.org/doc/221983

ER -

## References

top- P. Ambrož, Z. Masáková and E. Pelantová, Matrices of 3-iet preserving morphisms. Theoret. Comput. Sci.400 (2008) 113–136.
- P. Ambrož, Z. Masáková and E. Pelantová, Morphisms fixing words associated with exchange of three intervals. RAIRO – Theor. Inf. Appl.44 (2010) 3–17.
- P. Ambrož, A.E. Frid, Z. Masáková and E. Pelantová, On the number of factors in codings of three interval exchange. Discrete Math. Theoret. Comput. Sci.13 (2011) 51–66.
- P. Arnoux, V. Berthé, Z. Masáková and E. Pelantová, Sturm numbers and substitution invariance of 3iet words. Integers8 (2008) A14, 17.
- J. Berstel, Recent results in Sturmian words, in Developments in language theory II. Magdeburg (1995). World Sci. Publ., River Edge, NJ (1996) 13–24.
- J. Berstel and P. Séébold, Morphismes de sturm. Bull. Belg. Math. Soc.1 (1994) 175–189.
- J. Cassaigne, Sequences with grouped factors, in Developments in language theory III. Aristotle University of Thessaloniki, Greece (1998) 211–222.
- E.M. Coven and G.A. Hedlund, Sequences with minimal block growth. Math. Syst. Theor.7 (1973) 138–153.
- S. Ferenczi, C. Holton and L.Q. Zamboni, Structure of three-interval exchange transformations. II. A combinatorial description of the trajectories. J. Anal. Math.89 (2003) 239–276.
- L. Háková, Morphisms on generalized sturmian words. Master’s thesis, Czech Technical University in Prague (2008).
- A.B. Katok and A.M. Stepin, Approximations in ergodic theory. Uspehi Mat. Nauk22 (1967) 81–106.
- M. Lothaire, Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge 90 (2002).
- M. Morse and G.A. Hedlund, Symbolic dynamics II. Sturmian trajectories. Amer. J. Math.62 (1940) 1–42.
- P. Séébold, On the conjugation of standard morphisms. Theoret. Comput. Sci.195 (1998) 91–109.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.