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

School of Science

Waterford Institute of Technology

Ireland

**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.

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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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