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Morphisms fixing words associated with exchange of three intervals

Published online by Cambridge University Press:  11 February 2010

Petr Ambrož ,
Zuzana Masáková  and
Edita Pelantová
Petr Ambrož
Affiliation:
Doppler Institute & Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic; [email protected]; [email protected]; [email protected]
Zuzana Masáková
Affiliation:
Doppler Institute & Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic; [email protected]; [email protected]; [email protected]
Edita Pelantová
Affiliation:
Doppler Institute & Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic; [email protected]; [email protected]; [email protected]
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Abstract

We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.

Keywords

Interval exchange transformationSturmian morphismssubstitution invariance.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 1: Special issue dedicated to the 12th "Journées Montoises d'Informatique Théorique" , January 2010 , pp. 3 - 17
Copyright
© EDP Sciences, 2010

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