A general relation is presented for expressing any Young diagram as an operator polynomial acting on the Kronecker product formed from either the rows or columns of the original diagram. This relation is used to derive branching rules GH for compact groups G and H of GL(N) which are well suited for numerical computations. The examples chosen are the SU(3) contains/implies SO(3) and SU(4) contains/implies SU(2)*SU(2) reductions employed in studies of nuclear structure and the SU(8) contains/implies SU(3) decomposition employed in studies of particle physics.