Thue-Morse词的重复性度量
On repetitiveness measures of Thue-Morse words
摘要：
我们证明了对于任何$n\geq 4$，$n$ th Thue-Morse字$t_n$的最小字符串吸引子的大小$γ(t_n)$是4，反驳了Mantaci等人的猜想。[ICTCS 2019]它是$n$。我们还证明了$n \geq 3$的$δ(t_n) = \frac{10}{3+2^{4-n}}$，其中$δ(w)$是所有$k = 1,\ldots,|w|$中的最大值，$w$中长度为$k$的不同子串的数量除以$k$，这是Kociumaka等人最近研究的重复性度量。[拉丁语2020]。进一步证明了$t_n$的自参考Lempel-Ziv分解中因子的个数$z(t_n)$恰好是$2n$ .
英文摘要：
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 $2n$.
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