广义Thue-Morse词与回文丰富度
Generalized Thue-Morse words and palindromic richness
摘要：
我们证明了定义为$b \geq 2$和$m \geq 1$的广义Thue-Morse字$\mathbf{t}_{b,m}$为$\mathbf{t}_{b,m} = (s_b(n) \mod m)_{n=0}^{+\infty}$，其中$s_b(n)$表示整数$n$的基- $b$表示中的数字之和，在同构于由态射和反态射组成的$2m$阶二面体群的群$D_m$的所有元素下，它的语言是封闭的。考虑同时反态$Θ\in D_m$，我们表明，$\mathbf{t}_{b,m}$是饱和的$Θ$ -回文到最高可能的水平。利用作者和E。Pelantová，我们表明，$\mathbf{t}_{b,m}$是$D_m$丰富。我们还计算了$\mathbf{t}_{b,m}$的因子复杂度。
英文摘要：
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 $Θ\in D_m$, we show that $\mathbf{t}_{b,m}$ is saturated by $Θ$-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. Pelantová, we show that $\mathbf{t}_{b,m}$ is $D_m$-rich. We also calculate the factor complexity of $\mathbf{t}_{b,m}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
