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On the conjugation of Standard morphisms

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Mathematical Foundations of Computer Science 1996 (MFCS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1113))

Abstract

Let A={a, b} be an alphabet. An infinite word on A is Sturmian if it contains exactly n+1 distinct factors of length n for every integer n. A morphism f on A is Sturmian if f(x) is Sturmian whenever x is. A morphism on A is Standard if it is an element of the monoid generated by the two elementary morphisms E, which exchanges a and b, and φ, the Fibonacci morphism defined by φ(a)=ab and φ(b)=a. The set of Standard morphisms is a proper subset of the set of Sturmian morphisms. In the present paper, we give a characterization of Sturmian morphisms as conjugates of Standard ones. Sturmian words generated by Standard morphisms are characteristic words. The previous result allows to prove that a morphism f generates an infinite word having the same set of factors as a characteristic word generated by a Standard morphism g if and only if f is a conjugate of g.

Partially supported by PRC ”Mathématiques et Informatique” and by ESPRIT BRA working group 6317 - ASMICS 2.

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Authors and Affiliations

  1. LaRIA, Université de Picardie CURI, 5 rue du Moulin Neuf, F-80000, Amiens

    Patrice Séébold

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  1. Patrice Séébold
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Wojciech Penczek Andrzej Szałas

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© 1996 Springer-Verlag Berlin Heidelberg

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Séébold, P. (1996). On the conjugation of Standard morphisms. In: Penczek, W., Szałas, A. (eds) Mathematical Foundations of Computer Science 1996. MFCS 1996. Lecture Notes in Computer Science, vol 1113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61550-4_174

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  • DOI: https://doi.org/10.1007/3-540-61550-4_174

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61550-7

  • Online ISBN: 978-3-540-70597-0

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