  Permutation-symmetric n qubit pure states can be represented by n points on
the surface of the unit sphere by means of the Majorana representation. Here
this representation is employed to characterize and compare the three
entanglement classification schemes LOCC, SLOCC and the Degeneracy
Configuration. Symmetric SLOCC operations are found to be described by Mobius
transformations, and an intuitive visualization of their freedoms is presented.
For symmetric states of up to 5 qubits explicit forms of representative states
for all SLOCC classes are derived. The symmetric 4 qubit entanglement classes
are compared to the entanglement families introduced in [PRA 65, 052112
(2002)], and examples are given how the SLOCC-inequivalence of symmetric states
can be quickly determined from known results about Mobius transformations.
