Microscopic inclusion statistics in a discrete one-body spectrum

We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion statistics in which particles tend to coalesce more than ordinary bosons. We derive the microscopic occupation multiplicities of one-body quantum states and show that they factorize into a product of clusters of neighboring occupied states with enhanced statistical weights. Applying this statistics to a one-dimensional gas of particles in a harmonic well leads to a Calogero-like $n$-body inclusion spectrum with interesting physical properties.