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Identities induced by Riordan arrays

Morón, Manuel A. and Luzón, Ana and Merlini , Donatella and Sprugnoli, Renzo (2012) Identities induced by Riordan arrays. Linear Algebra and Applications, 436 (3). pp. 631-647. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379511005805

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Umbral calculus; Matrices; Variables; Riordan arrays; Recursive matrices; Combinatorial identities
Subjects:Sciences > Mathematics > Functions
Sciences > Mathematics > Algebra
ID Code:14834
Deposited On:18 Apr 2012 09:23
Last Modified:06 Feb 2014 10:10

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