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arXiv · 1804.05027

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

Paul Barry
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Abstract

We define and characterize the $γ$-matrix associated to 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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Paul Barry. 2018-04-13. The $γ$-Vectors of Pascal-like Triangles Defined by Riordan Arrays. https://arxiv.org/abs/1804.05027

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