On some problems related to palindrome closure
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 679-700.

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 $\vartheta$ is an involutory antimorphism of ${A}^{*}$, then the right and left $\vartheta$-palindromic closures of any factor of a $\vartheta$-standard word are also factors of some $\vartheta$-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.

DOI : https://doi.org/10.1051/ita:2007064
Classification : 68R15
Mots clés : palindromes, palindrome closures, sturmian and episturmian words, involutory antimorphisms, pseudopalindromes, pseudostandard words
@article{ITA_2008__42_4_679_0,
author = {Bucci, Michelangelo and Luca, Aldo de and Luca, Alessandro De and Zamboni, Luca Q.},
title = {On some problems related to palindrome closure},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {679--700},
publisher = {EDP-Sciences},
volume = {42},
number = {4},
year = {2008},
doi = {10.1051/ita:2007064},
zbl = {1155.68061},
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language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2007064/}
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Bucci, Michelangelo; Luca, Aldo de; Luca, Alessandro De; Zamboni, Luca Q. On some problems related to palindrome closure. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 679-700. doi : 10.1051/ita:2007064. http://www.numdam.org/articles/10.1051/ita:2007064/

[1] V. Anne, L.Q. Zamboni and I. Zorca, Palindromes and pseudo-palindromes in episturmian and pseudo-palindromic infinite words, in Words 2005, number 36 in Publications du LaCIM, edited by S. Brlek and C. Reutenauer (2005) 91-100.

[2] J. Berstel and D. Perrin, Theory of Codes. Academic Press (1985). | MR 797069 | Zbl 0587.68066

[3] J. Berstel and P. Séébold, Sturmian words, in Algebraic Combinatorics on Words, edited by M. Lothaire. Cambridge University Press, Cambridge UK (2002). Chapter 2. | MR 1905123

[4] M. Bucci, A. De Luca, A. De Luca and L.Q. Zamboni, On different generalizations of episturmian words. Theor. Comput. Sci., to appear. | MR 2397238 | Zbl 1136.68045

[5] A. De Luca, Sturmian words: structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183 (1997) 45-82. | MR 1468450 | Zbl 0911.68098

[6] A. De Luca and A. De Luca, Pseudopalindrome closure operators in free monoids. Theor. Comput. Sci. 362 (2006) 282-300. | MR 2259637 | Zbl 1101.68073

[7] X. Droubay, J. Justin and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy. Theor. Comput. Sci. 255 (2001) 539-553. | MR 1819089 | Zbl 0981.68126

[8] F. Durand, A characterization of substitutive sequences using return words. Discrete Mathematics 179 (1998) 89-101. | MR 1489074 | Zbl 0895.68087

[9] J. Justin, Episturmian morphisms and a Galois theorem on continued fractions. RAIRO-Theor. Inf. Appl. 39 (2005) 207-215. | Numdam | MR 2132588 | Zbl 1126.68519

[10] J. Justin and G. Pirillo, Episturmian words and episturmian morphisms. Theor. Comput. Sci. 276 (2002) 281-313. | MR 1896357 | Zbl 1002.68116

[11] L. Kari and K. Mahalingam, Watson-Crick conjugate and commutative words. Preliminary proceedings of DNA Computing 13, Memphis, USA. M.Garzon, H.Yan, Eds. (2007) 75-87. | Zbl 1137.68394

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