  We adapt here the computation of characters on incidence Hopf algebras
introduced by W. Schmitt in the 1990s to a family mixing bounded and unbounded
posets. We then apply our results to the family of hypertree posets and
partition posets. As a consequence, we obtain some enumerative formulas and a
new proof for the computation of the Moebius numbers of the hypertree posets.
Moreover, we compute the coproduct of the incidence Hopf algebra and recover a
known formula for the number of hypertrees with fixed valency set and edge
sizes set.
