  The sandwiched surface singularities are those rational surface singularities
which dominate birationally smooth surface singularities. de Jong and van
Straten showed that one can reduce the study of the deformations of a
sandwiched surface singularity to the study of deformations of a 1-dimensional
object, a so-called decorated plane curve singularity. In particular, the
Milnor fibers corresponding to their various smoothing components may be
reconstructed up to diffeomorphisms from those deformations of associated
decorated curves which have only ordinary singularities. Part of the topology
of such a deformation is encoded in the incidence matrix between the
irreducible components of the deformed curve and the points which decorate it,
well-defined up to permutations of columns. Extending a previous theorem
ofours, which treated the case of cyclic quotient singularities, we show that
the Milnor fibers which correspond to deformations whose incidence matrices are
different up to permutations of columns are not diffeomorphic in a strong
sense. This gives a lower bound on the number of Stein fillings of the contact
boundary of a sandwiched singularity.
