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- W2963819314 abstract "We prove that the generalized Thue-Morse word $mathbf{t}_{b,m}$ defined for $b geq 2$ and $m geq 1$ as $mathbf{t}_{b,m} = (s_b(n) mod m)_{n=0}^{+infty}$, 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 simultaneously 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 terminology generalizing the notion of palindromic richness for more antimorphisms recently introduced by the author and E. Pelantov'a, we show that $mathbf{t}_{b,m}$ is $D_m$-rich. We also calculate the factor complexity of $mathbf{t}_{b,m}$." @default.
- W2963819314 created "2019-07-30" @default.
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- W2963819314 date "2012-01-01" @default.
- W2963819314 modified "2023-10-17" @default.
- W2963819314 title "Generalized Thue-Morse words and palindromic richness" @default.
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