Relevant bibliographies by topics / Riordan arrays

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  2. Dissertations / Theses
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Academic literature on the topic 'Riordan arrays'

Author: Grafiati
Published: 10 March 2023
Last updated: 27 July 2025

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Journal articles on the topic "Riordan arrays"

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Barry, Paul. "Extensions of Riordan Arrays and Their Applications." Mathematics 13, no. 2 (2025): 242. https://doi.org/10.3390/math13020242.

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The Riordan group of Riordan arrays was first described in 1991, and since then, it has provided useful tools for the study of areas such as combinatorial identities, polynomial sequences (including families of orthogonal polynomials), lattice path enumeration, and linear recurrences. Useful extensions of the idea of a Riordan array have included almost Riordan arrays, double Riordan arrays, and their generalizations. After giving a brief overview of the Riordan group, we define two further extensions of the notion of Riordan arrays, and we give a number of applications for these extensions. T
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Barry, Paul. "Embedding Structures Associated with Riordan Arrays and Moment Matrices." International Journal of Combinatorics 2014 (March 17, 2014): 1–7. http://dx.doi.org/10.1155/2014/301394.

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Every ordinary Riordan array contains two naturally embedded Riordan arrays. We explore this phenomenon, and we compare it to the situation for certain moment matrices of families of orthogonal polynomials.
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Wang, Weiping, and Tianming Wang. "Generalized Riordan arrays." Discrete Mathematics 308, no. 24 (2008): 6466–500. http://dx.doi.org/10.1016/j.disc.2007.12.037.

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Luzón, Ana, Donatella Merlini, Manuel A. Morón, and Renzo Sprugnoli. "Complementary Riordan arrays." Discrete Applied Mathematics 172 (July 2014): 75–87. http://dx.doi.org/10.1016/j.dam.2014.03.005.

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Barry, Paul. "On the Connection Coefficients of the Chebyshev-Boubaker Polynomials." Scientific World Journal 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/657806.

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The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them.
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Merlini, Donatella, Douglas G. Rogers, Renzo Sprugnoli, and M. Cecilia Verri. "On Some Alternative Characterizations of Riordan Arrays." Canadian Journal of Mathematics 49, no. 2 (1997): 301–20. http://dx.doi.org/10.4153/cjm-1997-015-x.

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AbstractWe give several new characterizations of Riordan Arrays, the most important of which is: if {dn,k}n,k∈N is a lower triangular arraywhose generic element dn,k linearly depends on the elements in a well-defined though large area of the array, then {dn,k}n,k∈N is Riordan. We also provide some applications of these characterizations to the lattice path theory.
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O'Farrell, Anthony G. "Riordan Groups in Higher Dimensions." Mathematical Proceedings of the Royal Irish Academy 123A, no. 2 (2023): 95–124. http://dx.doi.org/10.1353/mpr.2023.a909312.

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Abstract: The classical Riordan groups associated to a given commutative ring are groups of infinite matrices (called Riordan arrays) associated to pairs of formal power series in one variable. The Fundamental Theorem of Riordan Arrays relates matrix multiplication to two group actions on such series, namely formal (convolution) multiplication and formal composition. We define the analogous Riordan groups involving formal power series in several variables, and establish the analogue of the Fundamental Theorem in that context. We discuss related groups of Laurent series and pose some questions.
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Lee, GwangYeon, and Mustafa Asci. "Some Properties of the(p,q)-Fibonacci and(p,q)-Lucas Polynomials." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/264842.

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Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called(p,q)-Fibonacci polynomials. We obtain combinatorial identities and by using Riordan method we get factorizations of Pascal matrix involving(p,q)-Fibonacci polynomials.
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Zhao, Xiqiang, and Shuangshuang Dings. "Sequences Related to Riordan Arrays." Fibonacci Quarterly 40, no. 3 (2002): 247–52. http://dx.doi.org/10.1080/00150517.2002.12428651.

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Luzón, Ana, Donatella Merlini, Manuel A. Morón, and Renzo Sprugnoli. "Identities induced by Riordan arrays." Linear Algebra and its Applications 436, no. 3 (2012): 631–47. http://dx.doi.org/10.1016/j.laa.2011.08.007.

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Dissertations / Theses on the topic "Riordan arrays"

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NOCENTINI, MASSIMO. "An algebraic and combinatorial study of some infinite sequences of numbers supported by symbolic and logic computation." Doctoral thesis, 2019. http://hdl.handle.net/2158/1217082.

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The subject of the thesis concerns the study of infinite sequences, in one or two dimensions, supporting the theoretical aspects with systems for symbolic and logic computation. In particular, in the thesis some sequences related to Riordan arrays are examined from both an algebraic and combinatorial points of view and also by using approaches usually applied in numerical analysis. Another part concerns sequences that enumerate particular combinatorial objects, such as trees, polyominoes, and lattice paths, generated by symbolic and certified computations; moreover, tiling problems and backtra
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Noble, Rob. "Zeros and Asymptotics of Holonomic Sequences." 2011. http://hdl.handle.net/10222/13298.

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In this thesis we study the zeros and asymptotics of sequences that satisfy linear recurrence relations with generally nonconstant coefficients. By the theorem of Skolem-Mahler-Lech, the set of zero terms of a sequence that satisfies a linear recurrence relation with constant coefficients taken from a field of characteristic zero is comprised of the union of finitely many arithmetic progressions together with a finite exceptional set. Further, in the nondegenerate case, we can eliminate the possibility of arithmetic progressions and conclude that there are only finitely many zero terms. Fo
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MERLINI, DONATELLA. "I Riordan Array nell'Analisi degli Algoritmi." Doctoral thesis, 1996. http://hdl.handle.net/2158/779171.

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Books on the topic "Riordan arrays"

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Riordan arrays : a primer - 1. edicion. Logic Press, 2016.

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Book chapters on the topic "Riordan arrays"

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Davenport, Dennis, Fatima Fall, Julian Francis, and Trinity Lee. "Production Matrices of Double Riordan Arrays." In Springer Proceedings in Mathematics & Statistics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-62166-6_7.

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Shapiro, Louis, Renzo Sprugnoli, Paul Barry, et al. "Characterization of Riordan Arrays by Special Sequences." In Springer Monographs in Mathematics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94151-2_4.

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Branch, Donovan, Dennis Davenport, Shakuan Frankson, Jazmin T. Jones, and Geoffrey Thorpe. "A & Z Sequences for Double Riordan Arrays." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-05375-7_3.

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He, Tian-Xiao. "Methods of Using Special Function Sequences, Number Sequences, and Riordan Arrays." In Methods for the Summation of Series, 5th ed. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003051305-4.

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