Morphisms preserving the set of words coding three interval exchange
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 107-122.

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.

DOI : 10.1051/ita/2012009
Classification : 68R15
Mots clés : interval exchange, three interval exchange, amicable sturmian morphisms, incidence matrix of morphism
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     title = {Morphisms preserving the set of words coding three interval exchange},
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Hejda, Tomáš. Morphisms preserving the set of words coding three interval exchange. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 107-122. doi : 10.1051/ita/2012009. http://www.numdam.org/articles/10.1051/ita/2012009/

[1] P. Ambrož, Z. Masáková and E. Pelantová, Matrices of 3-iet preserving morphisms. Theoret. Comput. Sci. 400 (2008) 113-136. | Zbl

[2] P. Ambrož, Z. Masáková and E. Pelantová, Morphisms fixing words associated with exchange of three intervals. RAIRO - Theor. Inf. Appl. 44 (2010) 3-17. | Numdam | MR | Zbl

[3] 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. | MR | Zbl

[4] P. Arnoux, V. Berthé, Z. Masáková and E. Pelantová, Sturm numbers and substitution invariance of 3iet words. Integers 8 (2008) A14, 17. | MR | Zbl

[5] J. Berstel, Recent results in Sturmian words, in Developments in language theory II. Magdeburg (1995). World Sci. Publ., River Edge, NJ (1996) 13-24. | MR | Zbl

[6] J. Berstel and P. Séébold, Morphismes de sturm. Bull. Belg. Math. Soc. 1 (1994) 175-189. | MR | Zbl

[7] J. Cassaigne, Sequences with grouped factors, in Developments in language theory III. Aristotle University of Thessaloniki, Greece (1998) 211-222.

[8] E.M. Coven and G.A. Hedlund, Sequences with minimal block growth. Math. Syst. Theor. 7 (1973) 138-153. | MR | Zbl

[9] 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. | MR | Zbl

[10] L. Háková, Morphisms on generalized sturmian words. Master's thesis, Czech Technical University in Prague (2008).

[11] A.B. Katok and A.M. Stepin, Approximations in ergodic theory. Uspehi Mat. Nauk 22 (1967) 81-106. | MR | Zbl

[12] M. Lothaire, Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge 90 (2002). | MR | Zbl

[13] M. Morse and G.A. Hedlund, Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62 (1940) 1-42. | JFM | MR

[14] P. Séébold, On the conjugation of standard morphisms. Theoret. Comput. Sci. 195 (1998) 91-109. | MR | Zbl

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