  We extend partition-theoretic work of Andrews, Bressoud, and Burge to
overpartitions, defining the notions of successive ranks, generalized Durfee
squares, and generalized lattice paths, and then relating these to
overpartitions defined by multiplicity conditions on the parts. This leads to
many new partition and overpartition identities, and provides a unification of
a number of well-known identities of the Rogers-Ramanujan type. Among these are
Gordon's generalization of the Rogers-Ramanujan identities, Andrews'
generalization of the G\"ollnitz-Gordon identities, and Lovejoy's ``Gordon's
theorems for overpartitions."
