Alonso Morón, ManuelLuzón, AnaMerlini, DonatellaSprugnoli, Renzo2023-06-202023-06-202012-02-01Luzón, A., Alonso Morón, M., Merlini, D., Sprugnoli, R. «Identities Induced by Riordan Arrays». Linear Algebra and Its Applications, vol. 436, n.o 3, febrero de 2012, pp. 631-47. DOI.org (Crossref), https://doi.org/10.1016/j.laa.2011.08.007.0024-379510.1016/j.laa.2011.08.007https://hdl.handle.net/20.500.14352/42104Historically, there exist two versions of the Riordan array concept. The older one (better known as recursive matrix) consists of bi-infinite matrices (d(n,k)) (n,k is an element of Z) (k > n implies d(n,k) = 0), deals with formal Laurent series and has been mainly used to study algebraic properties of such matrices. The more recent version consists of infinite, lower triangular arrays (d(n,k)) (n,k is an element of N) (k > n implies d(n,k) = 0), deals with formal power series and has been used to study combinatorial problems. Here we show that every Riordan array induces two characteristic combinatorial sums in three parameters n, k, m is an element of Z. These parameters can he specialized and generate an indefinite number of other combinatorial identities which are valid in the hi-infinite realm of recursive matrices.engjournal articlehttps//doi.org/10.1016/j.laa.2011.08.007http://www.sciencedirect.com/science/article/pii/S0024379511005805restricted access512.643517.5Umbral calculusMatricesVariablesRiordan arraysRecursive matricesCombinatorial identitiesFunciones (Matemáticas)Álgebra1202 Análisis y Análisis Funcional1201 Álgebra