Abstract: In recent years we have seen that several intriguing combinatorial identities, old and new, can be obtained by considering correspondences between certain interacting particle systems. Among these results, using a comparison between ASEP and the zero-range process, Balázs and Bowen were able to obtain a new proof of the Jacobi identity. A somewhat natural extension is to allow particles to interact with each other in a more general way. With this in mind we consider an Ising chain with inhomogeneous interactions and its mapping to a particle system with similarities to the zero-range process. This allows us to obtain new, and non-obvious, combinatorial identities relating to generating functions of certain types of partitions. Using the connection to the Ising model we are also able to obtain long-range reversible dynamics for a system of interacting particles on a half-infinite chain.