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Morphisms fixing words associated with exchange of three intervals

Petr AmbrožZuzana MasákováEdita Pelantová — 2010

RAIRO - Theoretical Informatics and Applications

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.

Palindromic complexity of infinite words associated with simple Parry numbers

Petr AmbrožZuzana MasákováEdita PelantováChristiane Frougny — 2006

Annales de l’institut Fourier

A simple Parry number is a real number β > 1 such that the Rényi expansion of 1 is finite, of the form d β ( 1 ) = t 1 t m . We study the palindromic structure of infinite aperiodic words u β that are the fixed point of a substitution associated with a simple Parry number β . It is shown that the word u β contains infinitely many palindromes if and only if t 1 = t 2 = = t m - 1 t m . Numbers β satisfying this condition are the so-called Pisot numbers. If t m = 1 then u β is an Arnoux-Rauzy word. We show that if β is a confluent Pisot number then 𝒫 ( n + 1 ) + 𝒫 ( n ) = 𝒞 ( n + 1 ) - 𝒞 ( n ) + 2 , where...

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