The γ-Vectors of Pascal-like Triangles Defined by Riordan Arrays
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.
Full version: pdf,
(Concerned with sequences
Received April 13 2018; revised version received December 19 2018.
Published in Journal of Integer Sequences,
December 19 2018.
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