Morphisms preserving the set of words coding three interval exchange. (English) Zbl 1247.68207

Summary: Any amicable pair \(\varphi , \psi \) of Sturmian morphisms enables a construction of a ternary morphism \(\eta \) 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\(^{\pm }(2,\mathbb N)\) and we study incidence matrices associated with the corresponding ternary morphisms \(\eta \).


68R15 Combinatorics on words
08A50 Word problems (aspects of algebraic structures)
Full Text: DOI arXiv EuDML


[1] P. Ambrož, Z. Masáková and E. Pelantová, Matrices of 3-iet preserving morphisms. Theoret. Comput. Sci.400 (2008) 113-136. · Zbl 1161.68042
[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. · Zbl 1186.68342
[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.
[4] P. Arnoux, V. Berthé, Z. Masáková and E. Pelantová, Sturm numbers and substitution invariance of 3iet words. Integers8 (2008) A14, 17. · Zbl 1202.11021
[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. · Zbl 1096.68689
[6] J. Berstel and P. Séébold, Morphismes de sturm. Bull. Belg. Math. Soc.1 (1994) 175-189. · Zbl 0803.68095
[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. · Zbl 0256.54028
[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. Zbl1130.37324 · Zbl 1130.37324
[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. Nauk22 (1967) 81-106. · Zbl 0172.07202
[12] M. Lothaire, Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge 90 (2002). · Zbl 1001.68093
[13] M. Morse and G.A. Hedlund, Symbolic dynamics II. Sturmian trajectories. Amer. J. Math.62 (1940) 1-42. · Zbl 0022.34003
[14] P. Séébold, On the conjugation of standard morphisms. Theoret. Comput. Sci.195 (1998) 91-109. · Zbl 0981.68104
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.