  We present positive maps and matrix inequalities for variables from the
positive cone. These inequalities contain partial transpose and reshuffling
operations, and can be understood as positive multilinear maps that are in
one-to-one correspondence with elements from the walled Brauer algebra. Using
our formalism, these maps can be obtained in a systematic and clear way by
manipulating partially transposed permutation operators under a partial trace.
Additionally, these maps are reasonably easy in construction by combining an
algorithmic approach with graphical calculus.
