Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-03T05:39:17.359Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  21 February 2012

Tomáš Hejda*
Affiliation:
Department of Mathematics FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic. [email protected]
Get access

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.

Type
Research Article
Copyright
© EDP Sciences 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ambrož, P., Masáková, Z. and Pelantová, E., Matrices of 3-iet preserving morphisms. Theoret. Comput. Sci. 400 (2008) 113136. Google Scholar
Ambrož, P., Masáková, Z. and Pelantová, E., Morphisms fixing words associated with exchange of three intervals. RAIRO – Theor. Inf. Appl. 44 (2010) 317. Google Scholar
Ambrož, P., Frid, A.E., Masáková, Z. and Pelantová, E., On the number of factors in codings of three interval exchange. Discrete Math. Theoret. Comput. Sci. 13 (2011) 5166. Google Scholar
Arnoux, P., Berthé, V., Masáková, Z. and Pelantová, E., Sturm numbers and substitution invariance of 3iet words. Integers 8 (2008) A14, 17. Google Scholar
J. Berstel, Recent results in Sturmian words, in Developments in language theory II. Magdeburg (1995). World Sci. Publ., River Edge, NJ (1996) 13–24.
Berstel, J. and Séébold, P., Morphismes de sturm. Bull. Belg. Math. Soc. 1 (1994) 175189. Google Scholar
J. Cassaigne, Sequences with grouped factors, in Developments in language theory III. Aristotle University of Thessaloniki, Greece (1998) 211–222.
Coven, E.M. and Hedlund, G.A., Sequences with minimal block growth. Math. Syst. Theor. 7 (1973) 138153. Google Scholar
Ferenczi, S., Holton, C. and Zamboni, L.Q., Structure of three-interval exchange transformations. II. A combinatorial description of the trajectories. J. Anal. Math. 89 (2003) 239276. Google Scholar
L. Háková, Morphisms on generalized sturmian words. Master’s thesis, Czech Technical University in Prague (2008).
Katok, A.B. and Stepin, A.M., Approximations in ergodic theory. Uspehi Mat. Nauk 22 (1967) 81106. Google Scholar
M. Lothaire, Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge 90 (2002).
Morse, M. and Hedlund, G.A., Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62 (1940) 142. Google Scholar
Séébold, P., On the conjugation of standard morphisms. Theoret. Comput. Sci. 195 (1998) 91109. Google Scholar