Properties of the ground-state, zero temperature 'phase diagram' of the Bose-Hubbard hamiltonian as understood by Fisher et al. [5] are studied using simple tools in the case of nite systems. The results obtained provide a transparent picture of the thermodynamic limit and reveal features reminiscent of shell structure in many-fermion systems. Independent sites and many-site correlations appear in correspondence with independent fermions and many-fermion correlations respectively. This paper is dedicated to Nicim Zagury, on the occasion of his seventieth birthday.
