Riordan矩阵族中的一个新的群：Sprugnoli群
A new group in the Riordan family of matrix groups: the Sprugnoli group
AI总结：
本文定义了一个由幂级数定义的下三角矩阵群，该群可以看作是普通Riordan群和双Riordan群的推广。该群的元素由三个幂级数定义，序列分割和垂直拉伸的Riordan数组在该群的构建中起重要作用。本文给出了该新群的生成矩阵特征，并指示了如何基于n元组的幂级数定义更高阶群。该群以Renzo Sprugnoli命名，以纪念他在将Riordan群应用于组合问题以及理解Riordan数组丰富结构方面的贡献。
摘要：
我们定义了一个由下三角矩阵组成的群，其列由幂级数定义。该群可以看作是普通Riordan群和双Riordan群的推广。该群的元素由三个幂级数定义。序列分割和垂直拉伸的Riordan数组在该群的构建中起重要作用。我们给出了该新群的生成矩阵特征。我们还指出了如何基于n元组的幂级数定义更高阶群。我们选择以Renzo Sprugnoli的名字命名该群，以纪念他在将Riordan群应用于组合问题以及理解Riordan数组丰富结构方面的贡献。
英文摘要：
We define a group of lower-triangular matrices whose columns are defined by power series. This group can be seen as a generalization of the (ordinary) Riordan group and the double Riordan group. Elements of this group are defined by three power series. Sequence bisections and vertically stretched Riordan arrays play an important role in the formulation of this group. We give a production matrix characterization of this new group. We also indicate how higher order groups can be defined, based on $n$-tuples of power series. We have chosen to name this group in memory of Renzo Sprugnoli, who was a pioneer in the application of the Riordan group to combinatorial problems as well as contributing to an understanding of the rich structure of Riordan arrays.
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