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Morphisms fixing words associatedwith 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; petr.ambroz@fjfi.cvut.cz; zuzana.masakova@fjfi.cvut.cz; edita.pelantova@fjfi.cvut.cz
Zuzana Masáková
Affiliation:
Doppler Institute & Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic; petr.ambroz@fjfi.cvut.cz; zuzana.masakova@fjfi.cvut.cz; edita.pelantova@fjfi.cvut.cz
Edita Pelantová
Affiliation:
Doppler Institute & Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic; petr.ambroz@fjfi.cvut.cz; zuzana.masakova@fjfi.cvut.cz; edita.pelantova@fjfi.cvut.cz
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Abstract

We consider words coding exchange of three intervals withpermutation (3,2,1), here called 3iet words. Recently, acharacterization of substitution invariant 3iet words wasprovided. We study the opposite question: what are the morphismsfixing a 3iet word? We reveal a narrow connection of suchmorphisms and morphisms fixing Sturmian words using the new notionof amicability.

Keywords

Interval exchange transformationSturmian morphismssubstitution invariance.

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