  Under the hypotheses of analyticity in the coupling constant, locality,
Lorentz covariance, and Poincare invariance of the deformations, combined with
the preservation of the number of derivatives on each field, the consistent
interactions between a collection of free massless tensor gauge fields with the
mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian
vector field, respectively a $p$-form gauge field, are addressed. The main
result is that a single mixed symmetry tensor field from the collection gets
coupled to the vector field/$p$-form. Our final result resembles to the well
known fact from General Relativity according to which there is one graviton in
a given world.
