论文标题
关于arnoux-rauzy单词的非重复复杂性
On non-repetitive complexity of Arnoux-Rauzy words
论文作者
论文摘要
The non-repetitive complexity $nr\mathcal{C}_{\bf u}$ and the initial non-repetitive complexity $inr\mathcal{C}_{\bf u}$ are functions which reflect the structure of the infinite word ${\bf u}$ with respect to the repetitions of factors of a given length.我们确定$ nr \ Mathcal {C} _ {\ bf u} $用于arnoux-rauzy单词和$ inr \ mathcal {c} _ {\ bf u} $用于标准arnoux-rauzy单词。我们的主要工具是Arnoux-rauzy单词的$ s $ - adic代表，并将其返回单词描述到其因素。然后，我们获得的公式用于评估$ nr \ mathcal {c} _ {\ bf u} $和$ inr \ mathcal {c} _ {\ bf u} $ for $ d $ bonacci Word。
The non-repetitive complexity $nr\mathcal{C}_{\bf u}$ and the initial non-repetitive complexity $inr\mathcal{C}_{\bf u}$ are functions which reflect the structure of the infinite word ${\bf u}$ with respect to the repetitions of factors of a given length. We determine $nr\mathcal{C}_{\bf u}$ for the Arnoux-Rauzy words and $inr\mathcal{C}_{\bf u}$ for the standard Arnoux-Rauzy words. Our main tools are $S$-adic representation of Arnoux-Rauzy words and description of return words to their factors. The formulas we obtain are then used to evaluate $nr\mathcal{C}_{\bf u}$ and $inr\mathcal{C}_{\bf u}$ for the $d$-bonacci word.
