  We use exact diagonalisation in order to study the infinite - $U$ limit of
the two dimensional Hubbard model. As well as looking at single-particle
correlations, such as $n_{{\bf k}\sigma }=\langle c^\dagger _{{\bf k}\sigma
}c_{{\bf k}\sigma } \rangle $, we also study {\it N-particle correlation
functions} which compare the relative positions of {\it all} the particles in
different models. In particular we study 16 and 18-site clusters and compare
the charge correlations in the Hubbard model with those of spinless fermions
and hard-core bosons. We find that although low densities of holes favour a
`locally-ferromagnetic' fermionic description, the correlations at larger
densities resemble those of pure hard-core bosons surprisingly well .
