  We systematically study the factorization and recursion relations in higher
genus correlation functions of BMN (Berenstein-Maldacena-Nastase) operators in
free N=4 super Yang Mills theory. These properties were found in a previous
paper by the author, and were conjectured to result from the correspondence
with type IIB string theory on the infinitely curved pp-wave background, where
the strings become effectively infinitely long. Here we push the calculations
to higher genus, provide more clarifications and verifications of the
factorization and recursion relations. Our calculations provide conjectural
indirect tests of the AdS/CFT correspondence for multi-loop superstring
amplitudes of stringy modes.
