Single Scale Analysis of Many Fermion Systems. Part 4: Sector Counting

For a two dimensional, weakly coupled system of fermions at temperature zero, one principal ingredient used to control the composition of the associated renormalization group maps is the careful counting of the number of quartets of sectors that are consistent with conservation of momentum. A similar counting argument is made to show that particle-particle ladders are irrelevant in the case of an asymmetric Fermi curve.