论文标题
关于thue-morse单词的重复措施
On repetitiveness measures of Thue-Morse words
论文作者
论文摘要
我们表明，$ n $ thue-morse word $ t_n $的尺寸$γ（t_n）$对于任何$ n \ geq 4 $ is t_n $ is 4 is is 4 $ is 4 $ is 4 $，否认了Mantaci等人的猜想。 [ICTCS 2019]是$ n $。 We also show that $δ(t_n) = \frac{10}{3+2^{4-n}}$ for $n \geq 3$, where $δ(w)$ is the maximum over all $k = 1,\ldots,|w|$, the number of distinct substrings of length $k$ in $w$ divided by $k$, which is a measure of repetitiveness recently studied by Kociumaka et al。 [拉丁2020]。此外，我们表明，$ t_n $的自我引用lempel-ziv分解中的数字$ z（t_n）$正好是$ 2N $。
We show that the size $γ(t_n)$ of the smallest string attractor of the $n$th Thue-Morse word $t_n$ is 4 for any $n\geq 4$, disproving the conjecture by Mantaci et al. [ICTCS 2019] that it is $n$. We also show that $δ(t_n) = \frac{10}{3+2^{4-n}}$ for $n \geq 3$, where $δ(w)$ is the maximum over all $k = 1,\ldots,|w|$, the number of distinct substrings of length $k$ in $w$ divided by $k$, which is a measure of repetitiveness recently studied by Kociumaka et al. [LATIN 2020]. Furthermore, we show that the number $z(t_n)$ of factors in the self-referencing Lempel-Ziv factorization of $t_n$ is exactly $2n$.
