Pomeron fan diagrams in perturbative QCD

Within QCD reggeon field theory we study the formation of two subsequent triple pomeron vertices in the process P$\to$PP$\to$PPP. We make use of an earlier investigation ~\cite{Bartels:1999aw} of the six-reggeon amplitude in deep inelastic scattering and show that in the large-$N_c$ limit pomeron fan diagrams emerge with the same triple pomeron vertex in all places. We thus confirm the BK-equation, but we also find additional terms related to the reggeization of the gluon, and we discuss their potential significance. Our analysis also includes the general pomeron $\to$ two odderon vertex: a particular version of this vertex has been included into earlier generalizations the BK equation.