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involutory antimorphisms

RAIRO - Theoretical Informatics and Applications (1)

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On some problems related to palindrome closure
Michelangelo Bucci, Aldo de Luca, Alessandro De Luca, Luca Q. Zamboni
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 42 / Issue 4 / October 2008

Published online by Cambridge University Press:

15 January 2008, pp. 679-700

Print publication:

October 2008
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In this paper, we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if ϑ is an involutory antimorphism of A*, then the right and left ϑ-palindromic closures of any factor of a ϑ-standard word are also factors of some ϑ-standard word. We also introduce the class of pseudostandard words with “seed”, obtained by iterated pseudopalindrome closure starting from a nonempty word. We show that pseudostandard words with seed are morphic images of standard episturmian words. Moreover, we prove that for any given pseudostandard word s with seed, all sufficiently long left special factors of s are prefixes of it.