(m, r)-CENTRAL RIORDAN ARRAYS AND THEIR APPLICATIONS

Tian-Xiao He, Sheng-liang Yang, Yan-Xue Xu

Research output: Journal ArticleArticlepeer-review

Abstract

Excerpt from the abstract:
It is known that the ( m, r )-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array G = ( d, h ) with h (0) = 0 and d (0), h (0) 6≠ 0, we obtain the generating function of its ( m, r )-central coefficients and give an explicit representation for the (m, r)-central Riordan array G (m,r) in terms of the Riordan array G . Meanwhile, the algebraic structures of the ( m, r )-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of m and r. As applications, we determine the ( m, r )-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach.
Original languageAmerican English
JournalCzechoslovak Mathematical Journal
Volume67
DOIs
StatePublished - Oct 2017

Keywords

  • Riordan array
  • central coefficient
  • central Riordan array
  • generating function
  • Fuss-Catalan number
  • Pascal matrix
  • Catalan matrix

Disciplines

  • Applied Mathematics
  • Mathematics

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