Decorating the gauge/YBE correspondence

In this paper, we aim to study the three-dimensional $N=2$ supersymmetric dual gauge theories on ${S}_{b}^{3}/{Z}_{r}$ in the context of the gauge/YBE correspondence. We consider hyperbolic integral identities acquired via the equality of supersymmetric lens partition functions as solutions to the decoration transformation and the flipping relation in statistical mechanics. The solutions of those transformations aim at investigating various decorated lattice models possessing the Boltzmann weights of integrable Ising-like models obtained via the gauge/YBE correspondence. We also constructed The Bailey pairs for the decoration transformation and the flipping relation.