Papers related to the Riordan matrices
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2016
  • G.-S. Cheon and J.-H. Jung, The $q$-Sheffer sequences of a new type and associated orthogonal polynomials, Linear Algebra Appl. 491 (2016) 171-186.
  • G.-S. Cheon, S.-T. Jin and L. W. Shapiro, A combinatorial equivalence relation for formal power series, Linear Algebra Appl. 491 (2016) 123-137.
  • H. Kim and R. P. Stanley, A refined enumeration of hex trees and related polynomials, European J. Comb. 54 (2016) 207-219.
  • G.-S. Cheon, H. Kim and L. W. Shapiro, A link between ordered trees and green-red trees, J. Korean Math. Soc. 53 (2016) 187-199.
2015
  • G.-S. Cheon and H. Kim, Representing polynomials as characteristic polynomials via the Stieltjes transform, Linear Algebra Appl. 476 (2015) 184-196.
2014
  • G.-S. Cheon, B. D. Choi and S.-T. Jin, An application of Riordan arrays to the transient analysis of M/M/1 queues, Appl. Math. Comput. 237 (2014) 659-671.
  • N. Tuglu, F. Yesil, E. G. Kocer and M. Dziemianczuk, The F-Analogue of Riordan Representation of Pascal Matrices via Fibonomial Coefficients, Journal of Applied Mathematics 2014 (2014) ID 841826.
2013
  • G.-S. Cheon and H. Kim, The elements of finite order in the Riordan group over the complex field, Linear Algebra Appl. 439 (2013) 4032-4046.
  • G.-S. Cheon and H. Kim, A new aspect of Hankel matrices via Krylov matrix, Linear Algebra Appl. 438 (2013) 361-373.
  • G.-S. Cheon, J.-H. Jung and Y. Lim, A $q$-analogue of the Riordan group, Linear Algebra Appl. 439 (2013) 4119-4129.
  • G.-S. Cheon, J.-H. Jung and L. W. Shapiro, Generalized Bessel numbers and some combinatorial settings, Discrete Math. 313 (2013) 2127-2138.
  • G.-S. Cheon and Y. Lim, Integral polynomial sequences arising from matrix powers of order 2, Linear Algebra Appl. 438 (2013) 269-287.
2012
  • G.-S. Cheon and J.-H. Jung, $r$-Whitney numbers of Dowling lattices, Discrete Math. 312 (2012) 2337-2348.
  • G.-S. Cheon and L. W. Shapiro, The uplift principle for ordered trees, Appl. Math. Lett. 25 (2012) 1010-1015.
  • G.-S. Cheon and I. M. Wanless, Some results towards the Dittert conjecture on permanents, Linear Algebra Appl. 436 (2012) 791-801.
  • G.-S. Cheon, H. Kim and L. W. Shapiro, Combinatorics of Riordan arrays with identical A and Z sequences, Discrete Math. 312 (2012) 2040-2049.
2011
  • G.-S. Cheon and T. Mansour, Rational combinations for the sums involving inverse binomial coefficients, Appl. Math. Comput. 218 (2011) 2641-2646.
  • G.-S. Cheon and S.-T. Jin, Structural properties of Riordan matrices and extending the matrices, Linear Algebra Appl. 435 (2011) 2019-2032.
  • G.-S. Cheon, H. Kim and L. W. Shapiro, The hitting time subgroup, ukasiewicz paths and Faber polynomials, Eur. J. Combin. 32 (2011) 82-91.
2010
  • G.-S. Cheon, H. Kim and L. W. Shapiro, An algebraic structure of Faber polynomials, Linear Algebra Appl. 433 (2010) 2019-2032.
  • G.-S. Cheon, S.-G. Lee and L. W. Shapiro, The Fine numbers refined, Eur. J. Combin. 31 (2010) 120-128.
2009
  • G.-S. Cheon, H. Kim and L. W. Shapiro, A generalization of Lucas polynomial sequence, Discrete Appl. Math. 157 (2009) 920-927.
  • G.-S. Cheon and A. W. Eckford, A relationship between subpermanents and the arithmetic-geometric mean inequality, Linear Algebra Appl. 430 (2009) 114-120.
  • G.-S. Cheon, S.-T. Jin, H. Kim and L. W. Shapiro, Riordan group involutions and the -sequence, Discrete Appl. Math. 157 (2009) 1696-1701.
2008
  • P. Barry, A note on Krawtchouk polynomials and Riordan arrays, J. of Integer Sequences 11 (2008) 08.2.2..
  • G.-S. Cheon, and M. E. A. El-Mikkawy, Generalized harmonic numbers with Riordan arrays, J. of Number Theory 128 (2008) 413-425.
  • G.-S. Cheon, and H. Kim, Simple proofs of open problems about the structure of involutions in the Riordan group, Linear Algebra and its Applications 428 (2008) 930-940.
  • D. Merlini, Proper generating trees and their internal path length, Discrete Applied Mathematics 156 (2008) 627-646.
  • G.-S. Cheon and L. W. Shapiro, Protected points in ordered trees, Appl. Math. Lett. 21 (2008) 516-520.
  • D. Baccherini, D. Merlini, and R. Sprugnoli, Level generating trees and proper Riordan arrays, Applicable Analysis and Discrete Mathematics 2 (2008) 69-91.
  • G.-S. Cheon, H. Kim, and L. W. Shapiro, Riordan group involutions, Linear Algebra and its Applications 428 (2008) 941-952.
2007
  • Y.-D. Sun, and C.Jia, Counting Dyck paths with strictly increasing peak sequences, J. Math. Res. Exposition 27 (2007) 253-263.
  • P. Barry, and P. Fitzpatrick, On a one-parameter family of Riordan arrays and the weight distribution of MDS codes, J. of Integer Sequences 9 (2007) 07.9.8..
  • P. Barry, On a family of generalized Pascal triangles defined by exponential Riordan arrays, J. of Integer Sequences 10 (2007) 07.3.5..
  • W. Y. C. Chen, N. Y. Li, L. W. Shapiro, and S. H. F.Yan, Matrix identities on weighted partial Motzkin paths, European J. Combinatorics 28 (2007) 1196-1207.
  • J. L. Diaz-Barrero, J. Gibergans-Baguena, and P. G. Popescu, Some identities involving rational sums, Applicable Analysis and Discrete Mathematics 1 (2007) 397-402.
  • T. X. He, L. C. Hsu, and P. J.-S. Shiue, The Sheffer Group and the Riordan Group, Discrete Applied Mathematics 155 (2007) 1895-1909.
  • P. Barry, Some observations on the Lah and Laguerre transforms of integer sequences, J. of Integer Sequences 10 (2007) 07.4.6..
  • D. Merlini,and R. Sprugnoli, Playing with some identities of Andrews, J. of Integer Sequences 10 (2007) 07.9.5..
2006
  • G.-S. Cheon, M. E. A. El-Mikkawy, and H.-G. Seol, New identities for Stirling numbers via Riordan arrays, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math 13 (2006) 311-318.
  • D. Merlini, R. Sprugnoli, and M. C. Verri, The Cauchy numbers, Discrete Mathematics 306 (2006) 1906-1920.
  • D. Merlini, R. Sprugnoli, and M. C. Verri, Combinatorial inversions and implicit Riordan arrays, Electronic Notes on Discrete Mathematics - Combinatorics 2006 26 (2006) 103-110.
2005
  • N. T. Cameron, and A. Nkwanta, On some (pseudo) involutions in the Riordan group, J. of Integer Sequences 8 (2005) 05.3.7..
  • M. C. Wilson, Asymptotics for generalized Riordan arrays, 2005 Int. Conf. on Analysis of Algorithms - Discrete Math. Theor. Comput. Sci. Proc AD (2005) 323-333.
  • D. Merlini, R. Sprugnoli, and M. C. Verri, The Akiyama-Tanigawa transformation, Integers 5 (2005) A5.
  • G. P. Egorychev, and E. V. Zima, Decomposition and group theoretic characterization of pairs of inverse relations of the Riordan type, Acta Applicandae Mathematicae 85 (2005) 93-109.
  • E. Munarini, Enumeration of order ideals of a garland, Ars Combinatorica 76 (2005) 185-192.
  • W.-J. Woan, and D. Hough, Lattice paths and subgroups of Riordan group, Congressus Numerantium 177 (2005) 45-49.
  • A. Nkwanta, and L. W. Shapiro, Pell walks and Riordan matrices, Fibonacci Quarterly 43 (2005) 170-180.
  • P. Peart, W.-J. Woan, and B. Tankersley, Algebraic and combinatorial interpretations of the Genocchi triangle, Congressus Numerantium 175 (2005) 45-51.
  • L. W. Shapiro, The average is one, Congressus Numerantium 176 (2005) 3-10.
  • P. Barry, A Catalan transform and related transformations on integer sequences, J. of Integer Sequences 8 (2005) 05.4.5..
2004
  • D. Merlini, R. Sprugnoli, and M. C. Verri, Waiting patterns for a printer, Discrete Applied Mathematics 144 (2004) 359-373.
  • D. Merlini, F. Uncini, and M. C. Verri, A unified approach to the study of general and palindromic compositions, Integers 4 (2004) A23.
  • M. Tan, and T. Wang, Lah matrix and its algebraic properties, Ars Combinatorica 70 (2004) 97-108.
  • X. Zhao, S. Ding, and T. Wang, Some summation rules related to the Riordan arrays, Discrete Mathematics 281 (2004) 295-307.
2003
  • A. Nkwanta, A Riordan matrix approach to unifying a selected class of combinatorial arrays, Congressus Numerantium 160 (2003) 33-45.
  • L. W.Shapiro, Bijections and the Riordan group, Theoretical Computer Science 307 (2003) 403-413.
  • X. Zhao, and T. Wang, Some identities related to reciprocal functions, Discrete Mathematics 265 (2003) 323-335.
  • D. H. Yin, Riordan array / partial monoid, J. Math. Res. Exposition 23 (2003) 253-260.
  • D. S. Hough, and L. W. Shapiro, The noncrossing descent matrix is Riordan, Congressus Numerantium 162 (2003) 83-96.
2002
  • I-C. Huang, Inverse relations and Schauder bases, J. Combin. Theory Ser. A 97 (2002) 203-224.
  • D. Merlini, and R. Sprugnoli, A Riordan array proof of a curious identity, Integers 2 (2002) A8.
  • W. Lang, On polynomials related to derivatives of the generating function of Catalan numbers, Fibonacci Quarterly 40 (2002) 299-313.
  • D. Li, and S. Shang, Several computing formulas for combinatorial sums, Appl. Math. J. Chinese Univ. Ser. B 17 (2002) 119-124.
  • L. W. Shapiro, Catalan trigonometry, Congressus Numerantium 156 (2002) 129-136.
  • Q.-W. Zhang, and X.-R. Ma, The ordinary Bailey lemma and Riordan chain, J. Math. Res. Exposition 22 (2002) 401-406.
  • X. Zhao, and S. Ding, Sequences related to Riordan arrays, Fibonacci Quarterly 40 (2002) 247-252.
  • D. Merlini, R. Sprugnoli, and M. C. Verri, The tennis ball problem, J. Combinatorial Theory Ser. A 99 (2002) 307-344.
2001
  • X. Q. Zhao, Y. F. Zhang and A. W. Liang, A method of forming normal Riordan matrices(chinese), J. Luoyang Univ. 4 (2001) 4-5.
  • L. W. Shapiro, Some open questions about random walks, involutions, limiting distributions, and generating functions, Advances in Applied Mathematics 27 (2001) 585-596.
Before 2000
  • P. Peart, and W.-J. Woan, A divisibility property for a subgroup of Riordan matrices, Discrete Applied Mathematics 98 (2000) 255-263.
  • D. Merlini, and M. C. Verri, Generating trees and proper Riordan arrays, Descrete Mathematics 218 (2000) 167-183.
  • P. Peart, and W.-J. Woan, Generating functions via Hankel and Stieltjes matrices, J. of Integer Sequences 3 (2000) 00.2.1..
  • M. Aigner, Catalan-like numbers and determinants, J. of Combinatorial Theory Ser. A 87 (1999) 33-51.
  • A. Nkwanta, and N. Knox, A note on Riordan matrices, African Americans in Mathematics II (1999) 99-107.
  • M. Aigner, A characterization of Bell numbers, Discrete Mathematics 205 (1999) 207-210.
  • D. S. Yin, Riordan groups and three generalized identities, J. Dalian Univ. Tech. 39 (1999) 6-11.
  • X. R. Ma, Inverse chains of the Riordan group and their applications to combinatorial sums(chinese), J. Math. Res. Exposition 19 (1999) 445-451.
  • X. R. Ma, A generaliuzation of the Kummer identity and its application to Fibonacci-Lucas sequences, FibonacciQuarterly 36 (1998) 339-347.
  • C. Corsani, D. Merliniand R. Sprugnoli, Left inversion of combinatorial sums, Discrete Mathematics 180 (1998) 107-122.
  • D. Merlini, D. G. Rogers, R. Sprugnoli, and M. C. Verri, On some alternative characterizations of Riordan arrays, Canadian J. Mathematics 49 (1997) 301-320.
  • D. Merlini, R. Sprugnoli, and M. C. Verri, A uniform model for the storage utilization of B-tree-like structures, Information Processing Letters 57 (1996) 53-58.
  • S. Getu, and L.W. Shapiro, Lattice paths and Bessel functions, Congressus Numerantium 108 (1995) 161-169.
  • R. Sprugnoli, Riordan arrays and the Abel-Gould identity, Discrete Mathematics 142 (1995) 213-233.
  • L. W. Shapiro, A survey of the Riordan Group, Talk at a meeting of the American Mathematical Society Richmond, Virginia (1994) .
  • D. Merlini, R. Sprugnoli, and M. C. Verri, Algebraic and combinatorial properties of simple, coloured walks, Trees in Algebra and Programming - LNCS 787 (1994) 218-233.
  • R. Sprugnoli, Riordan arrays and combinatorial sums, Discrete Mathematics 132 (1994) 267-290.
  • P. Peart, and L. Woodson, Triple factorization of some Riordan matrices, Fibonacci Quarterly 31 (1993) 121-128.
  • L. W. Shapiro, S. Getu, W.-J. Woan, and L. Woodson, The Riordan group, Discrete Applied Mathematics 34 (1991) 229-239.
  • D. G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Mathematics 22 (1978) 301-310.