Palindromes in Infinite Ternary Words

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F09%3A00164376" target="_blank" >RIV/68407700:21340/09:00164376 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Palindromes in Infinite Ternary Words
Original language description
We study infinite words u over an alphabet A satisfying the property (P): P(n) + P(n + 1) = 1 + #A for any non-negative integer 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+1for any positive integer 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 positive integer 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).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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