Palindromes in infinite ternary words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 4, pp. 687-702.

We study infinite words 𝐮 over an alphabet 𝒜 satisfying the property 𝒫:𝒫(n)+𝒫(n+1)=1+#𝒜 for any n, where 𝒫(n) denotes the number of palindromic factors of length n occurring in the language of 𝐮. We study also infinite words satisfying a stronger property 𝒫ℰ: every palindrome of 𝐮 has exactly one palindromic extension in 𝐮. For binary words, the properties 𝒫 and 𝒫ℰ coincide and these properties characterize sturmian words, i.e., words with the complexity 𝒞(n)=n+1 for any n. In this paper, we focus on ternary infinite words with the language closed under reversal. For such words 𝐮, we prove that if 𝒞(n)=2n+1 for any n, then 𝐮 satisfies the property 𝒫 and moreover 𝐮 is rich in palindromes. Also a sufficient condition for the property 𝒫ℰ is given. We construct a word demonstrating that 𝒫 on a ternary alphabet does not imply 𝒫ℰ.

DOI : https://doi.org/10.1051/ita/2009016
Classification : 68R15
Mots clés : ternary infinite words, palindromes, generalized sturmian words, rich words
@article{ITA_2009__43_4_687_0,
     author = {Balkov\'a, L'ubom{\'\i}ra and Pelantov\'a, Edita and Starosta, \v{S}t\v{e}p\'an},
     title = {Palindromes in infinite ternary words},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {687--702},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {4},
     year = {2009},
     doi = {10.1051/ita/2009016},
     zbl = {1191.68476},
     mrnumber = {2589989},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2009016/}
}
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Balková, L'ubomíra; Pelantová, Edita; Starosta, Štěpán. Palindromes in infinite ternary words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 4, pp. 687-702. doi : 10.1051/ita/2009016. http://www.numdam.org/articles/10.1051/ita/2009016/

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