  The current article considers Mayer cluster integrals of n-dimensional hard
particles in the n>1 dimensional flat Euclidean space. Extending results from
Wertheim and Rosenfeld, we proof that the graphs are completely reducible into
1- and 2-point measures, with algebraic rules similar to Feynman diagrams in
quantum field theory. The hard-particle partition function reduces then to a
perturbative solvable problem.
