  The $N$-qubit Dicke states $|D^N_k\rangle$, of Hamming-weight $k$, are a
class of entangled states which play an important role in quantum algorithm
optimization. We present a general calculation of entanglement entropy in Dicke
states, which we use to describe the $|D^N_k\rangle$ entropy cone. We
demonstrate that all $|D^N_k\rangle$ entropy vectors emerge symmetrized, and
use this to define a min-cut protocol on star graphs which realizes
$|D^N_k\rangle$ entropy vectors. We identify the stabilizer group for all
$|D^N_k\rangle$, under the action of the $N$-qubit Pauli group and two-qubit
Clifford group, which we use to construct $|D^N_k\rangle$ reachability graphs.
We use these reachability graphs to analyze and bound the evolution of
$|D^N_k\rangle$ entropy vectors in Clifford circuits.
