A Riordan array family for some integrable lattice models

TL;DR

This paper introduces a new family of Riordan arrays linked to integrable lattice models, providing explicit formulas and factorizations, and connecting them to Robbins numbers and the 20 vertex model.

Contribution

It presents a novel Riordan array family with explicit formulas and factorizations, connecting combinatorial arrays to integrable lattice models.

Findings

Arrays generate Robbins numbers and 20 vertex model sequences

Closed-form expressions for array elements

Canonical Catalan factorizations provided

Abstract

We study a family of Riordan arrays whose square symmetrizations lead to the Robbins numbers as well as numbers associated to the $20$ vertex model. We provide closed-form expressions for the elements of these arrays, and also give a canonical Catalan factorization for them. We describe a related family of Riordan arrays whose symmetrizations also lead to the same integer sequences.