  We explore the groundstates of a few dipolar bosons in optical lattices with
incommensurate filling. The competition of kinetic, potential, and interaction
energies leads to the emergence of a variety of crystal state orders with
characteristic one- and two-body densities. We probe the transitions between
these orders and construct the emergent state diagram as a function of the
dipolar interaction strength and the lattice depth. We show that the crystal
state orders can be observed using the full distribution functions of the
particle number extracted from simulated single-shot images.
