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Published in:
2024 | OriginalPaper | Chapter
Production Matrices of Double Riordan Arrays
Authors : Dennis Davenport, Fatima Fall, Julian Francis, Trinity Lee
Published in: Combinatorics, Graph Theory and Computing
Publisher: Springer Nature Switzerland
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Abstract
A double Riordan array is an infinite lower triangular matrix, denoted by \( (g; f_1, f_2)\), where g, \(f_1\), and \(f_2\) are generating functions. The coefficients of the generating function g gives the first column of the matrix, and the remaining columns are found by multiplying the previous column by alternating \(f_1\) and \(f_2\). In other words, This is the columns construction of a double Riordan array. We can determine the elements of a double Riordan array using A- and Z-sequences which gives a row construction of a double Riordan array, see ([2] and [5]). In this chapter we define the production matrix of a double Riordan array, and show how it can be used to determine the A- and Z-sequences.
$$\displaystyle (g; f_1, f_2)=(g, gf_1, gf_1f_2,g{f_1}^2f_2, gf_1^2f_2^2,\dots ). $$
