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.
Mots clés : interval exchange, three interval exchange, amicable sturmian morphisms, incidence matrix of morphism
@article{ITA_2012__46_1_107_0,
author = {Hejda, Tom\'a\v{s}},
title = {Morphisms preserving the set of words coding three interval exchange},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {107--122},
publisher = {EDP-Sciences},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/ita/2012009},
mrnumber = {2904964},
zbl = {1247.68207},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2012009/}
}
TY - JOUR AU - Hejda, Tomáš TI - Morphisms preserving the set of words coding three interval exchange JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 107 EP - 122 VL - 46 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2012009/ DO - 10.1051/ita/2012009 LA - en ID - ITA_2012__46_1_107_0 ER -
%0 Journal Article %A Hejda, Tomáš %T Morphisms preserving the set of words coding three interval exchange %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 107-122 %V 46 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2012009/ %R 10.1051/ita/2012009 %G en %F ITA_2012__46_1_107_0
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] , and , Matrices of 3-iet preserving morphisms. Theoret. Comput. Sci. 400 (2008) 113-136. | Zbl
[2] , and , Morphisms fixing words associated with exchange of three intervals. RAIRO - Theor. Inf. Appl. 44 (2010) 3-17. | Numdam | MR | Zbl
[3] , , and , On the number of factors in codings of three interval exchange. Discrete Math. Theoret. Comput. Sci. 13 (2011) 51-66. | MR | Zbl
[4] , , and , Sturm numbers and substitution invariance of 3iet words. Integers 8 (2008) A14, 17. | MR | Zbl
[5] , 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] and , Morphismes de sturm. Bull. Belg. Math. Soc. 1 (1994) 175-189. | MR | Zbl
[7] , Sequences with grouped factors, in Developments in language theory III. Aristotle University of Thessaloniki, Greece (1998) 211-222.
[8] and , Sequences with minimal block growth. Math. Syst. Theor. 7 (1973) 138-153. | MR | Zbl
[9] , and , Structure of three-interval exchange transformations. II. A combinatorial description of the trajectories. J. Anal. Math. 89 (2003) 239-276. | MR | Zbl
[10] , Morphisms on generalized sturmian words. Master's thesis, Czech Technical University in Prague (2008).
[11] and , Approximations in ergodic theory. Uspehi Mat. Nauk 22 (1967) 81-106. | MR | Zbl
[12] , Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge 90 (2002). | MR | Zbl
[13] and , Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62 (1940) 1-42. | JFM | MR
[14] , On the conjugation of standard morphisms. Theoret. Comput. Sci. 195 (1998) 91-109. | MR | Zbl
Cité par Sources :
