2024/10/14 by Frankson, Shakuan
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2410.10709
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 kth column of a Riordan array is given by the function gfk. The Double Riordan group is defined similarly using three generating functions g, f1, and f2, where g is an even function and f1 and f2 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.