lY σ=1 Nσ mσ # ln   lQ σ=1 D/l mσ lQ σ=1 Nσ mσ   (S43) The symmetry refined upper bound to the entropy then becomes S(M) max(N1, . . . , Nl) = ′X m1,...,ml

Size of a block In the case of D/l sites on the lattice, since all sites can accommodate fermions with any σ internal label, we haveD/l mσ ways to arrange the mσ fermions with inte