2026-06-28T10:03:04Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/421042024-07-08T15:59:35Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Alonso Morón, Manuel
author
Luzón, Ana
author
Merlini, Donatella
author
Sprugnoli, Renzo
2023-06-20T00:09:41Z
2023-06-20T00:09:41Z
2012-02-01
Luzón, 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.
0024-3795
10.1016/j.laa.2011.08.007
https://hdl.handle.net/20.500.14352/42104
https//doi.org/10.1016/j.laa.2011.08.007
http://www.sciencedirect.com/science/article/pii/S0024379511005805
Historically, 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.
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Identities induced by Riordan arrays
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