1 results
Palindromes in infinite ternary words
-
- Journal:
- RAIRO - Theoretical Informatics and Applications / Volume 43 / Issue 4 / October 2009
- Published online by Cambridge University Press:
- 15 September 2009, pp. 687-702
- Print publication:
- October 2009
-
- Article
- Export citation
-
We study infinite words u over an alphabet $\mathcal{A}$
satisfying the property $\mathcal{P} :~\mathcal{P}(n)+\mathcal{P}(n+1) = 1+ \#\mathcal{A}\ {\rm for\ any}\ n \in\mathbb{N}$ 
, where $\mathcal{P}(n)$ 
denotes the number ofpalindromic factors of length n occurring in the language of u.We study also infinite words satisfying a strongerproperty $\mathcal{PE}$ 
: every palindrome of u has exactly one palindromic extension in u. For binary words, the properties $\mathcal{P}$ 
and $\mathcal{PE}$ 
coincide and these properties characterize Sturmian words, i.e.,words with the complexity C(n) = n + 1 for any $n \in \mathbb{N}$ 
. In this paper, we focus on ternary infinite wordswith the language closed under reversal. For such words u,we prove that if C(n) = 2n + 1 for any $n \in \mathbb{N}$ 
,then u satisfies the property $\mathcal{P}$ andmoreover u is rich in palindromes. Also a sufficient condition for the property $\mathcal{PE}$ is given.We construct a word demonstrating that $\mathcal{P}$ on a ternaryalphabet does not imply $\mathcal{PE}$ .
