  In this paper we study the relation between long cycles and Bose-Condensation
in the Infinite range Bose-Hubbard Model with a hard core interaction. We
calculate the density of particles on long cycles in the thermodynamic limit
and find that the existence of a non-zero long cycle density coincides with the
occurrence of Bose-Einstein condensation but this density is not equal to that
of the Bose condensate.
