Scalar products of Bethe vectors in the models with $gl(m|n)$ symmetry

We study scalar products of Bethe vectors in the models solvable by thenested algebraic Bethe ansatz and described by $\mathfrak{gl}(m|n)$superalgebra. Using coproduct properties of the Bethe vectors we obtain a sumformula for their scalar products. This formula describes the scalar product interms of a sum over partitions of Bethe parameters. We also obtain recursionsfor the Bethe vectors. This allows us to find recursions for the highestcoefficient of the scalar product