Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 301394, 7 pages
http://dx.doi.org/10.1155/2014/301394
Research Article

Embedding Structures Associated with Riordan Arrays and Moment Matrices

School of Science, Waterford Institute of Technology, Waterford, Ireland

Received 17 December 2013; Accepted 14 February 2014; Published 17 March 2014

Academic Editor: Toufik Mansour

Copyright © 2014 Paul Barry. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. W. Shapiro, S. Getu, W.-J. Woan, and L. C. Woodson, “The Riordan group,” Discrete Applied Mathematics, vol. 34, no. 1–3, pp. 229–239, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. C. Corsani, D. Merlini, and R. Sprugnoli, “Left-inversion of combinatorial sums,” Discrete Mathematics, vol. 180, no. 1–3, pp. 107–122, 1998. View at Google Scholar · View at Scopus
  3. R. Sprugnoli, “Riordan arrays and combinatorial sums,” Discrete Mathematics, vol. 132, no. 1–3, pp. 267–290, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. P. Barry and A. Hennessy, “Meixner-type results for Riordan arrays and associated integer sequences,” Journal of Integer Sequences, vol. 13, no. 9, article 10.9.4, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. P. Barry, “Riordan arrays, orthogonal polynomials as moments, and Hankel transforms,” Journal of Integer Sequences, vol. 14, no. 2, article 11.2.2, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. G.-S. Cheon, H. Kim, and L. W. Shapiro, “Riordan group involutions,” Linear Algebra and Its Applications, vol. 428, no. 4, pp. 941–952, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. D. E. Davenport, L. W. Shapiro, and L. C. Woodson, “The double Riordan group,” The Electronic Journal of Combinatorics, vol. 18, no. 2, Paper 33, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T.-X. He and R. Sprugnoli, “Sequence characterization of Riordan arrays,” Discrete Mathematics, vol. 309, no. 12, pp. 3962–3974, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. S.-T. Jin, “A characterization of the Riordan Bell subgroup by C-sequences,” The Korean Journal of Mathematics, vol. 17, no. 2, pp. 147–154, 2009. View at Google Scholar
  10. D. Merlini, D. G. Rogers, R. Sprugnoli, and M. C. Verri, “On some alternative characterizations of Riordan arrays,” Canadian Journal of Mathematics, vol. 49, no. 2, pp. 301–320, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, NY, USA, 1978. View at MathSciNet
  12. W. Gautschi, Orthogonal Polynomials: Computation and Approximation, Clarendon Press, Oxford, UK, 2004. View at MathSciNet
  13. G. Szegö, Orthogonal Polynomials, American Mathematical Society, Providence, RI, USA, 4th edition, 1975.
  14. E. Deutsch, L. Ferrari, and S. Rinaldi, “Production matrices,” Advances in Applied Mathematics, vol. 34, no. 1, pp. 101–122, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. E. Deutsch, L. Ferrari, and S. Rinaldi, “Production matrices and Riordan arrays,” Annals of Combinatorics, vol. 13, no. 1, pp. 65–85, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. H. S. Wall, Analytic Theory of Continued Fractions, AMS Chelsea, New York, NY, USA, 1967.
  17. N. J. A. Sloane, “The On-Line Encyclopedia of Integer Sequences,” 2011, http://oeis.org.
  18. N. J. A. Sloane, “The on-line Encyclopedia of Integer Sequences,” Notices of the American Mathematical Society, vol. 50, no. 8, pp. 912–915, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet