  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.
