  We characterize metrologically useful multipartite entanglement by
representing partitions with Young diagrams. We derive entanglement witnesses
that are sensitive to the shape of Young diagrams and show that Dyson's rank
acts as a resource for quantum metrology. Common quantifiers, such as the
entanglement depth and $k$-separability are contained in this approach as the
diagram's width and height. Our methods are experimentally accessible in a wide
range of atomic systems, as we illustrate by analyzing published data on the
quantum Fisher information and spin-squeezing coefficients.
