  We present a generalization, which we call (k,m)-rank, of Dyson's notion of
rank to integer partitions with k successive Durfee rectangles and give two
combinatorial symmetries associated with this new definition. We prove these
symmetries bijectively. Using the two symmetries we give a new combinatorial
proof of generalized Roger-Ramanujan identities. We also describe the
relationship between (k,m)-rank and Garvan's k-rank.
