Kinematic Superstructures for Abnormal Couplings in Multipion Dual Amplitudes

The problem of including abnormally coupled trajectories (the $\omega -A_2$ trajectory) in the multipion dual amplitude is analyzed in detail. A procedure for analyzing kinematic superstructures for including these trajectories is presented and the appropriate three-particle vertices are discussed. As examples of constructing the "minimal" dual amplitudes, the minimal sets of superstructures are given explicitly for the $6\pi$ and $8\pi$ amplitudes.