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

DOI : https://doi.org/10.1051/ita:2007064
Classification:  68R15
Keywords: 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},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {4},
     year = {2008},
     pages = {679-700},
     doi = {10.1051/ita:2007064},
     zbl = {1155.68061},
     mrnumber = {2458701},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2008__42_4_679_0}
}
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, Volume 42 (2008) no. 4, pp. 679-700. doi : 10.1051/ita:2007064. http://www.numdam.org/item/ITA_2008__42_4_679_0/

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