  Lagrangian descriptions of irreducible and reducible integer higher-spin
representations of the Poincare group subject to a Young tableaux
$Y[\hat{s}_1,\hat{s}_2]$ with two columns are constructed within a metric-like
formulation in a $d$-dimensional flat space-time on the basis of a BRST
approach extending the results of [arXiv:1412.0200[hep-th]]. A
Lorentz-invariant resolution of the BRST complex within both the constrained
and unconstrained BRST formulations produces a gauge-invariant Lagrangian
entirely in terms of the initial tensor field $\Phi_{[\mu]_{\hat{s}_1},
[\mu]_{\hat{s}_2}}$ subject to $Y[\hat{s}_1,\hat{s}_2]$ with an additional
tower of gauge parameters realizing the $(\hat{s}_1-1)$-th stage of
reducibility with a specific dependence on the value
$(\hat{s}_1-\hat{s}_2)=0,1,...,\hat{s}_1$. Minimal BRST--BV action is
suggested, being proper solution to the master equation in the minimal sector
and providing objects appropriate to construct interacting Lagrangian
formulations with mixed-antisymmetric fields in a general framework.
