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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.
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