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On some problems related to palindrome closure

Published online by Cambridge University Press:  15 January 2008

Michelangelo Bucci ,
Aldo de Luca ,
Alessandro De Luca  and
Luca Q. Zamboni
Michelangelo Bucci
Affiliation:
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II. Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy; micbucci@unina.it; aldo.deluca@unina.it; alessandro.deluca@unina.it
Aldo de Luca
Affiliation:
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II. Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy; micbucci@unina.it; aldo.deluca@unina.it; alessandro.deluca@unina.it
Alessandro De Luca
Affiliation:
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II. Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy; micbucci@unina.it; aldo.deluca@unina.it; alessandro.deluca@unina.it
Luca Q. Zamboni
Affiliation:
Department of Mathematics, PO Box 311430, University of North Texas. Denton TX, USA; luca@unt.edu
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Abstract

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.

Keywords

Palindromespalindrome closuresSturmian and episturmian wordsinvolutory antimorphismspseudopalindromespseudostandard words.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 4: Fibonacci words , October 2008 , pp. 679 - 700
Copyright
© EDP Sciences, 2008

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References

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