On the abelian complexity of the Rudin-Shapiro sequence
On the abelian complexity of the Rudin-Shapiro sequence
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鲁丁·夏皮罗序列的阿贝尔复杂性
DOI：
10.1016/j.jmaa.2017.02.019
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发表时间：
2017
影响因子：
1.3
通讯作者：
Wu Wen
中科院分区：
文献类型：
--
作者：
Lu Xiaotao;Chen Jin;Wen Zhixiong;Wu Wen
本文研究了Rudin Shapiro序列及其相关序列的阿贝尔复杂性。我们证明了这两个序列共享相同的复杂性函数p（n），它满足一定的递归关系。因此，阿贝尔复杂度函数是2-正则的。进一步证明了渐近函数$\lambda（x）$的图的盒维数为3/2，其中$\lambda（x）= \lim_{k\to\infity}\rho（4^kx）/\root{4^kx}$且对任意x > 0$，$\rho（x）= p（[x]）$.
In this paper, we study the abelian complexity of the Rudin Shapiro sequence and a related sequence. We show that these two sequences share the same complexity function p(n), which satisfies certain recurrence relations. As a consequence, the abelian complexity function is 2-regular. Further,.we prove that the box dimension of the graph of the asymptotic function $\lambda(x)$ is 3/2, .where $\lambda(x) = \lim_{k\to\infity}\rho(4^k x)/\root{4^k x}$ and $\rho(x) = p([x])$ for every $x > 0$.