Doubling of the cylinder contribution in the topological expansion and Pomeron-f identity

This note examines how the various intermediate-state configurations and different regions of phase space contribute to building up the planar and cylinder contributions of the topological expansion. Various factors of 2 are generated on the planar and cylinder level. For the cylinder, the doubling mechanism is different depending on whether the number of intermediate-state clusters is even or odd. Despite the cylinder doubling, the Pomeron-f identity is retained