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arXiv · 2410.10709

Finding an Isomorphism between the Riordan Group and a Subgroup of the Double Riordan Group

Shakuan Frankson
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Abstract

The Riordan group is a set of infinite lower-triangular matrices defined by two generating functions, $g$ and $f$. The elements of the group are called Riordan arrays, denoted by $(g,f)$, and the $k$th column of a Riordan array is given by the function $gf^k$. The Double Riordan group is defined similarly using three generating functions $g$, $f_1$, and $f_2$, where $g$ is an even function and $f_1$ and $f_2$ are odd functions. This group generalizes the Checkerboard subgroup of the Riordan group, where $g$ is even and $f$ is odd. An open question posed by Davenport, Shapiro, and Woodson was if there exists an isomorphism between the Riordan group and a subgroup of the Double Riordan group. This question is answered in this article.

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Shakuan Frankson. 2024-10-14. Finding an Isomorphism between the Riordan Group and a Subgroup of the Double Riordan Group. https://arxiv.org/abs/2410.10709

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