Production matrices

Riordan arrays and d-orthogonality

“…has exponential generating function e x . We will use the following [13,14], important result concerning matrices that are production matrices for exponential Riordan arrays.…”

“…The Riordan array (13) is the coefficient array of the modified d-orthogonal Chebyshev polynomials of the second kind given by…”

Recurrence relations for the Sheffer sequences

“…For an invertible lower triangular matrix R, its production matrix (also called its Stieltjes matrix, see [4,10]) is the matrix P = R −1 R, where R is the matrix R with its first row removed. The production matrix P can be characterized by the matrix equality RP = DR, where D = (δ i+1,j ) i,j 0 (δ is the usual Kronecker delta).…”

On the equivalence problem for succession rules

“…Determining the generating function of a given system is not always an easy task [1]. Therefore, some recent papers focused on the development of some algebraic tools in order to study enumerative properties of succession rules, without computing the corresponding generating functions, by using a linear operator approach [11], or production matrices [9].…”