  We consider the problem of characterizing genuine multiparticle entanglement
for permutationally invariant states using the approach of PPT mixtures. We
show that the evaluation of this necessary biseparability criterion scales
polynomially with the number of particles. In practice, it can be evaluated
easily up to ten qubits and improves existing criteria significantly. Finally,
we show that our approach solves the problem of characterizing genuine
multiparticle entanglement for permutationally invariant three-qubit states.
