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Academic literature on the topic 'Riordan arrays'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Riordan arrays"

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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 (December 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 (April 1, 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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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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Luzón, Ana, Donatella Merlini, Manuel A. Morón, and Renzo Sprugnoli. "Identities induced by Riordan arrays." Linear Algebra and its Applications 436, no. 3 (February 2012): 631–47. http://dx.doi.org/10.1016/j.laa.2011.08.007.

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He, Tian-Xiao. "Matrix characterizations of Riordan arrays." Linear Algebra and its Applications 465 (January 2015): 15–42. http://dx.doi.org/10.1016/j.laa.2014.09.008.

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Krelifa, Ali, and Ebtissem Zerouki. "Riordan arrays and d-orthogonality." Linear Algebra and its Applications 515 (February 2017): 331–53. http://dx.doi.org/10.1016/j.laa.2016.11.039.

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Sprugnoli, Renzo. "Riordan arrays and combinatorial sums." Discrete Mathematics 132, no. 1-3 (September 1994): 267–90. http://dx.doi.org/10.1016/0012-365x(92)00570-h.

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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 backtracking techniques are studied in depth and enumeration of recursive structures are also given. We propose a preliminary suite of tools to interact with the Online Encyclopedia of Integer Sequences, providing a crawling facility to download sequences recursively according to their cross references, pretty-printing them and, finally, drawing graphs representing their connections. In the context of automatic proof derivation, an extension to an automatic theorem prover is proposed to support the relational programming paradigm. This allows us to encode facts about combinatorial objects and to enumerate the corresponding languages by producing certified theorems at the same time. As a concrete illustration, we provide many chunks of code written using functional programming languages; our focus is to support theoretical derivations using sound, clear and elegant implementations to check their validity.
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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. For generally nonconstant coefficients, there are generalizations of this theorem due to Bézivin and to Methfessel that imply, under fairly general conditions, that we obtain a finite union of arithmetic progressions together with an exceptional set of density zero. Further, a condition is given under which one can exclude the possibility of arithmetic progressions and obtain a set of zero terms of density zero. In this thesis, it is shown that this condition reduces to the nondegeneracy condition in the case of constant coefficients. This allows for a consistent definition of nondegeneracy valid for generally nonconstant coefficients and a unified result is obtained. The asymptotic theory of sequences that satisfy linear recurrence relations with generally nonconstant coefficients begins with the basic theorems of Poincaré and Perron. There are some generalizations of these theorems that hold in greater generality, but if we restrict the coefficient sequences of our linear recurrences to be polynomials in the index, we obtain full asymptotic expansions of a predictable form for the solution sequences. These expansions can be obtained by applying a transfer method of Flajolet and Sedgewick or, in some cases, by applying a bivariate method of Pemantle and Wilson. In this thesis, these methods are applied to a family of binomial sums and full asymptotic expansions are obtained. The leading terms of the expansions are obtained explicitly in all cases, while in some cases a field containing the asymptotic coefficients is obtained and some divisibility properties for the asymptotic coefficients are obtained using a generalization of a method of Stoll and Haible.
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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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Shapiro, Louis, Renzo Sprugnoli, Paul Barry, Gi-Sang Cheon, Tian-Xiao He, Donatella Merlini, and Weiping Wang. "Characterization of Riordan Arrays by Special Sequences." In Springer Monographs in Mathematics, 69–99. Cham: 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, 33–46. Cham: 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, 193–304. 5th ed. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003051305-4.

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