论文标题
关于Riordan阵列的中心描述
On the Central Description of the Group of Riordan Arrays
论文作者
论文摘要
我们通过使用$ \ sum_ {n = 0}^{\ infty} g_n x^n $的两个功率系列的两个功率系列来提供Riordan数组组的替代描述，其中$ g_0 \ ne 0 $来构建构造组的典型元素。我们将这些元素与通常描述中的Riordan数组相关联，表明每个新构造的元素都是“常规”元素的垂直半部分。由于与Riordan阵列的核心系数链接，我们称之为“中心”描述的产品规则和反向的构建是在此新描述中给出的。这是针对普通生成功能的情况进行的。最后，我们简要查看指数案例。
We provide an alternative description of the group of Riordan arrays, by using two power series of the form $\sum_{n=0}^{\infty} g_n x^n$, where $g_0 \ne 0$ to build a typical element of the constructed group. We relate these elements to Riordan arrays in the usual description, showing that each newly constructed element is the vertical half of a "usual" element. The product rules and the construction of the inverse are given in this new description, which we call a "central" description, because of links to the central coefficients of Riordan arrays. This is done for the case of ordinary generating functions. Finally, we briefly look at the exponential case.
