The γ-vectors of pascal-like triangles defined by riordan arrays

Paul Barry

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1 Citation (Scopus)

Abstract

We define and characterize the γ-matrix associated with Pascal-like matrices that are defined by ordinary and exponential Riordan arrays. We also define and characterize the γ-matrix of the reversions of these triangles, in the case of ordinary Riordan arrays. We are led to the γ-matrices of a one-parameter family of generalized Narayana triangles. Thus these matrices generalize the matrix of γ-vectors of the associahedron. The principal tools used are the bivariate generating functions of the triangles and Jacobi continued fractions.

Original languageEnglish
Article number19.1.4
JournalJournal of Integer Sequences
Volume22
Issue number1
Publication statusPublished - 2019

Keywords

  • Associahedron
  • Eulerian number
  • Gamma vector
  • Narayana number
  • Pascal-like triangle
  • Permutahedron
  • Riordan array

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