论文标题
关于Rueppel序列和相关Hankel决定因素的一些观察结果
Some observations on the Rueppel sequence and associated Hankel determinants
论文作者
论文摘要
从基于加泰罗尼亚数字的定义开始，我们对Rueppel序列进行了经验研究。我们将Hankel变换用作主要技术。通过这种转换，我们找到了诸如雅各比序列和纸折叠序列等序列的链接。我们还研究了该序列定义的几个数阵列，它们是重要的加泰罗尼亚三角形的类似物。我们确定了与Golay-Rudin-Shapiro序列相关的序列，该序列在将论文的汉克尔变换与经典序列联系起来方面起着基本作用。如果在莱布尼茨公式中出现某些特权排列以确保决定因素具有特殊作用，则举例说明了一个例子。
Starting with a definition based on the Catalan numbers, we carry out an empirical study of the Rueppel sequence. We use the Hankel transform as the main technique. By means of this transform we find links to such sequences as the Jacobi sequence and the paper-folding sequence. We also study several number arrays defined by this sequence, which are analogs of the important Catalan triangles of combinatorics. We identify a sequence related to the Golay-Rudin-Shapiro sequence that plays a fundamental role in linking the Hankel transforms of the paper with classical sequences. Examples are given where certain privileged permutations appearing in the Leibnitz formula for determinants have a special role.
