Journal of Integer Sequences, Vol. 22 (2019), Article 19.1.4

The γ-Vectors of Pascal-like Triangles Defined by Riordan Arrays

Paul Barry
School of Science
Waterford Institute of Technology


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.

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(Concerned with sequences A000108 A000898 A001263 A001591 A007318 A008288 A008292 A055151 A059344 A077938 A100861 A100862 A101280 A271875.)

Received April 13 2018; revised version received December 19 2018. Published in Journal of Integer Sequences, December 19 2018.

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