论文标题
在Riordan阵列的总和，衍生物和翻转上
On Sums, Derivatives, and Flips of Riordan Arrays
论文作者
论文摘要
我们研究了三个关于Riordan阵列的操作。首先，我们调查了Riordan阵列的总和何时产生另一个Riordan阵列。我们表征了这些Riordan阵列的$ A $ - - 和$ z $ - 序列，并在Riordan阵列的总和不产生Riordan阵列时，还标识了$ a $ sequiness的模拟。此外，我们在Riordan阵列上定义了新操作“ der”和“翻转”。我们充分表征了这些操作所产生的Riordan阵列，这些操作应用于Riordan组的Appell和Lagrange子组。最后，我们研究了这些操作在各种已知的Riordan阵列中的应用，在此过程中产生了许多组合身份。
We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the $A$- and $Z$-sequences of these sums of Riordan arrays, and also identify an analog for $A$-sequences when the sum of Riordan arrays does not yield a Riordan array. In addition, we define the new operations `Der' and `Flip' on Riordan arrays. We fully characterize the Riordan arrays resulting from these operations applied to the Appell and Lagrange subgroups of the Riordan group. Finally, we study the application of these operations to various known Riordan arrays, generating many combinatorial identities in the process.
