Geodesic
Generalized Thue-Morse words and palindromic richness
Kybernetika, Tome 48 (2012) no. 3, pp. 361-370.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We prove that the generalized Thue-Morse word $\mathbf{t}_{b,m}$ defined for $b \ge 2$ and $m \ge 1$ as $\mathbf{t}_{b,m} = \left ( s_b(n) \mod m \right )_{n=0}^{+\infty}$, where $s_b(n)$ denotes the sum of digits in the base-$b$ representation of the integer $n$, has its language closed under all elements of a group $D_m$ isomorphic to the dihedral group of order $2m$ consisting of morphisms and antimorphisms. Considering antimorphisms $\Theta \in D_m$, we show that $\mathbf{t}_{b,m}$ is saturated by $\Theta$-palindromes up to the highest possible level. Using the generalisation of palindromic richness recently introduced by the author and E. Pelantová, we show that $\mathbf{t}_{b,m}$ is $D_m$-rich. We also calculate the factor complexity of $\mathbf{t}_{b,m}$.
Classification : 68R15
Keywords: palindrome; palindromic richness; Thue-Morse; Theta-palindrome 
@article{KYB_2012__48_3_a1,
     author = {Starosta, \v{S}t\v{e}p\'an},
     title = {Generalized {Thue-Morse} words and palindromic richness},
     journal = {Kybernetika},
     pages = {361--370},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2012},
     mrnumber = {2975794},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a1/}
}
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Starosta, Štěpán. Generalized Thue-Morse words and palindromic richness. Kybernetika, Tome 48 (2012) no. 3, pp. 361-370. http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a1/