论文标题
关于Rudin-Shapiro序列的最大自相关
On maximal autocorrelations of Rudin-Shapiro sequences
论文作者
论文摘要
在本文中，我们提供了另一种证据，表明$ m $ -th rudin -shapiro sequence的最大大道自相关的顺序与$λ^{m} $的顺序相同，其中$λ$是$ x^{3} + x^{2} + x^{2} {2} - 2x-2x-2x-2x-2x-4 $的真实根。该结果最初是由Allouche，Choi，Denise，Erdélyi和Saffari（2019）和Choi（2020）证明了这一结果的证明，并使用该问题转换为线性代数。我们的方法简化了这种线性代数翻译，并提供了另一种处理Choi给出的计算的方法。此外，我们证明了$ m $ -th rudin-shapiro序列的最大周期性自相关的类似结果。最后，我们讨论了给定的证据与关节频谱半径理论之间的联系，以及自相关最大的猜想。
In this paper, we present an alternative proof showing that the maximal aperiodic autocorrelation of the $m$-th Rudin-Shapiro sequence is of the same order as $λ^{m}$, where $λ$ is the real root of $x^{3} + x^{2} - 2x - 4$. This result was originally proven by Allouche, Choi, Denise, Erdélyi, and Saffari (2019) and Choi (2020) using a translation of the problem into linear algebra. Our approach simplifies this linear algebraic translation and provides another method of dealing with the computations given by Choi. Additionally, we prove an analogous result for the maximal periodic autocorrelation of the $m$-th Rudin-Shapiro sequence. We conclude with a discussion on the connection between the proofs given and joint spectral radius theory, as well as a couple of conjectures on which autocorrelations are maximal.
