Copartitions

We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers–Ramanujan partitions, theta functions, mock theta functions, partitions with parts separated by parity, and crank statistics. Using both analytic and combinatorial methods, we give two forms of the three-parameter generating function, and we study several special cases that demonstrate the potential broader impact the study of copartitions may have.