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Journal articles on the topic 'Riordan arrays'

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Author: Grafiati

Published: 10 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Deutsch, Emeric, Luca Ferrari, and Simone Rinaldi. "Production Matrices and Riordan Arrays." Annals of Combinatorics 13, no. 1 (May 8, 2009): 65–85. http://dx.doi.org/10.1007/s00026-009-0013-1.

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12

He, Tian-Xiao, and Renzo Sprugnoli. "Sequence characterization of Riordan arrays." Discrete Mathematics 309, no. 12 (June 2009): 3962–74. http://dx.doi.org/10.1016/j.disc.2008.11.021.

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13

Chen, Xi, Huyile Liang, and Yi Wang. "Total positivity of Riordan arrays." European Journal of Combinatorics 46 (May 2015): 68–74. http://dx.doi.org/10.1016/j.ejc.2014.11.009.

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14

Sprugnoli, Renzo. "Combinatorial sums through Riordan arrays." Journal of Geometry 101, no. 1-2 (August 2011): 195–210. http://dx.doi.org/10.1007/s00022-011-0090-2.

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15

Agapito, José, Ângela Mestre, Pasquale Petrullo, and Maria M. Torres. "A symbolic treatment of Riordan arrays." Linear Algebra and its Applications 439, no. 7 (October 2013): 1700–1715. http://dx.doi.org/10.1016/j.laa.2013.05.007.

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16

Mu, Lili, Jianxi Mao, and Yi Wang. "Row polynomial matrices of Riordan arrays." Linear Algebra and its Applications 522 (June 2017): 1–14. http://dx.doi.org/10.1016/j.laa.2017.02.006.

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17

Wang, Weiping, and Chenlu Zhang. "Riordan arrays and related polynomial sequences." Linear Algebra and its Applications 580 (November 2019): 262–91. http://dx.doi.org/10.1016/j.laa.2019.06.008.

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18

Cheon, Gi-Sang, and M. E. A. El-Mikkawy. "Generalized harmonic numbers with Riordan arrays." Journal of Number Theory 128, no. 2 (February 2008): 413–25. http://dx.doi.org/10.1016/j.jnt.2007.08.011.

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19

Wang, Weiping. "Riordan arrays and harmonic number identities." Computers & Mathematics with Applications 60, no. 5 (September 2010): 1494–509. http://dx.doi.org/10.1016/j.camwa.2010.06.031.

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20

Merlini, Donatella, and M. Cecilia Verri. "Generating trees and proper Riordan Arrays." Discrete Mathematics 218, no. 1-3 (May 2000): 167–83. http://dx.doi.org/10.1016/s0012-365x(99)00343-x.

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21

Burlachenko, E. V. "Riordan arrays and generalized Lagrange series." Mathematical Notes 100, no. 3-4 (September 2016): 531–39. http://dx.doi.org/10.1134/s0001434616090248.

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22

Merlini, Donatella, Renzo Sprugnoli, and Maria Cecilia Verri. "Combinatorial sums and implicit Riordan arrays." Discrete Mathematics 309, no. 2 (January 2009): 475–86. http://dx.doi.org/10.1016/j.disc.2007.12.039.

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23

Merlini, Donatella, Renzo Sprugnoli, and Maria Cecilia Verri. "Combinatorial inversions and implicit Riordan arrays." Electronic Notes in Discrete Mathematics 26 (September 2006): 103–10. http://dx.doi.org/10.1016/j.endm.2006.08.019.

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24

Xi, Gao Wen, Lan Long, Xue Quan Tian, and Zhao Hui Chen. "Inverse Generalized Harmonic Numbers with Riordan Arrays." Advanced Materials Research 842 (November 2013): 750–53. http://dx.doi.org/10.4028/www.scientific.net/amr.842.750.

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In this paper, By observing that the infinite triangle obtained from some generalized harmonic numbers follows a Riordan array, we obtain connections between the Stirling numbers of both kinds and other inverse generalized harmonic numbers. Further, we proved some combinatorial sums and inverse generalized harmonic number identities.

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25

Yang, Lin, and Sheng-Liang Yang. "Riordan arrays, Łukasiewicz paths and Narayana polynomials." Linear Algebra and its Applications 622 (August 2021): 1–18. http://dx.doi.org/10.1016/j.laa.2021.03.012.

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26

Ma, Qianqian, and Weiping Wang. "Riordan arrays and r-Stirling number identities." Discrete Mathematics 346, no. 1 (January 2023): 113211. http://dx.doi.org/10.1016/j.disc.2022.113211.

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27

Baccherini, D., D. Merlini, and R. Sprugnoli. "Level generating trees and proper Riordan arrays." Applicable Analysis and Discrete Mathematics 2, no. 1 (2008): 69–91. http://dx.doi.org/10.2298/aadm0801069b.

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28

Zhu, Bao-Xuan. "Total Positivity from the Exponential Riordan Arrays." SIAM Journal on Discrete Mathematics 35, no. 4 (January 2021): 2971–3003. http://dx.doi.org/10.1137/20m1379952.

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29

Cheon, Gi-Sang, and Sung-Tae Jin. "The group of multi-dimensional Riordan arrays." Linear Algebra and its Applications 524 (July 2017): 263–77. http://dx.doi.org/10.1016/j.laa.2017.03.010.

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30

Sprugnoli, Renzo. "Riordan arrays and the Abel-Gould identity." Discrete Mathematics 142, no. 1-3 (July 1995): 213–33. http://dx.doi.org/10.1016/0012-365x(93)e0220-x.

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31

Merlini, Donatella, and Renzo Sprugnoli. "Arithmetic into geometric progressions through Riordan arrays." Discrete Mathematics 340, no. 2 (February 2017): 160–74. http://dx.doi.org/10.1016/j.disc.2016.08.017.

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32

Yang, Sheng-Liang, Yan-Xue Xu, and Tian-Xiao He. "$(m,r)$-central Riordan arrays and their applications." Czechoslovak Mathematical Journal 67, no. 4 (October 24, 2017): 919–36. http://dx.doi.org/10.21136/cmj.2017.0165-16.

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33

Barry, Paul. "Riordan arrays, generalized Narayana triangles, and series reversion." Linear Algebra and its Applications 491 (February 2016): 343–85. http://dx.doi.org/10.1016/j.laa.2015.10.032.

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34

He, Tian-Xiao, and Louis W. Shapiro. "Row sums and alternating sums of Riordan arrays." Linear Algebra and its Applications 507 (October 2016): 77–95. http://dx.doi.org/10.1016/j.laa.2016.05.035.

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35

Chen, Xi, and Yi Wang. "Notes on the total positivity of Riordan arrays." Linear Algebra and its Applications 569 (May 2019): 156–61. http://dx.doi.org/10.1016/j.laa.2019.01.015.

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36

Słowik, R. "Some (counter)examples on totally positive Riordan arrays." Linear Algebra and its Applications 594 (June 2020): 117–23. http://dx.doi.org/10.1016/j.laa.2020.02.021.

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37

Zhao, Xiqiang, Shuangshuang Ding, and Tingming Wang. "Some summation rules related to the Riordan arrays." Discrete Mathematics 281, no. 1-3 (April 2004): 295–307. http://dx.doi.org/10.1016/j.disc.2003.08.007.

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38

Xi, Gao Wen, and Zheng Ping Zhang. "Summations of Inverse Generalized Harmonic Numbers with Riordan Arrays." Applied Mechanics and Materials 687-691 (November 2014): 1394–98. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.1394.

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By observing that the infinite triangle obtained from some generalized harmonic numbers follows a Riordan array, we using connections between the Stirling numbers of both kinds and other inverse generalized harmonic numbers. we proved some combinatorial sums and inverse generalized harmonic number identities.

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39

Petrullo, P. "Palindromic Riordan arrays, classical orthogonal polynomials and Catalan triangles." Linear Algebra and its Applications 618 (June 2021): 158–82. http://dx.doi.org/10.1016/j.laa.2021.02.007.

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40

He, Tian-Xiao. "Sequence characterizations of double Riordan arrays and their compressions." Linear Algebra and its Applications 549 (July 2018): 176–202. http://dx.doi.org/10.1016/j.laa.2018.03.029.

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41

Cheon, Gi-Sang, and Minho Song. "A new aspect of Riordan arrays via Krylov matrices." Linear Algebra and its Applications 554 (October 2018): 329–41. http://dx.doi.org/10.1016/j.laa.2018.05.028.

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42

Baccherini, D., D. Merlini, and R. Sprugnoli. "Binary words excluding a pattern and proper Riordan arrays." Discrete Mathematics 307, no. 9-10 (May 2007): 1021–37. http://dx.doi.org/10.1016/j.disc.2006.07.023.

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43

Yang, Sheng-liang, and Sai-nan Zheng. "A Determinant Expression for the Generalized Bessel Polynomials." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/242815.

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Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.

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44

Słowik, R. "More about involutions in the group of almost-Riordan arrays." Linear Algebra and its Applications 624 (September 2021): 247–58. http://dx.doi.org/10.1016/j.laa.2021.04.016.

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45

Mao, Jianxi, Lili Mu, and Yi Wang. "Yet another criterion for the total positivity of Riordan arrays." Linear Algebra and its Applications 634 (February 2022): 106–11. http://dx.doi.org/10.1016/j.laa.2021.11.005.

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46

Cheon, Gi-Sang, Hana Kim, and Louis W. Shapiro. "Combinatorics of Riordan arrays with identical A and Z sequences." Discrete Mathematics 312, no. 12-13 (July 2012): 2040–49. http://dx.doi.org/10.1016/j.disc.2012.03.023.

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47

Ju, Hyeong-Kwan, Hyun-Jeong Lee, and Soo-Jeong Seo. "INTEGRAL POLYNOMIAL SEQUENCES RELATED WITH KRAWTCHOUK MATRICES AND ASSOCIATED RIORDAN ARRAYS." Honam Mathematical Journal 34, no. 3 (September 25, 2012): 297–310. http://dx.doi.org/10.5831/hmj.2012.34.3.297.

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48

He, Tian-Xiao. "Riordan arrays associated with Laurent series and generalized Sheffer-type groups." Linear Algebra and its Applications 435, no. 6 (September 2011): 1241–56. http://dx.doi.org/10.1016/j.laa.2011.03.004.

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49

Yang, Sheng-Liang, Yan-Ni Dong, Tian-Xiao He, and Yan-Xue Xu. "A unified approach for the Catalan matrices by using Riordan arrays." Linear Algebra and its Applications 558 (December 2018): 25–43. http://dx.doi.org/10.1016/j.laa.2018.07.037.

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50

Cheon, Gi-Sang, Bong Dae Choi, and Sung-Tae Jin. "An application of Riordan arrays to the transient analysis of queues." Applied Mathematics and Computation 237 (June 2014): 659–71. http://dx.doi.org/10.1016/j.amc.2014.03.142.

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