  We compute the characteristic polynomials of the posets of hypertrees. We
show that the generating series of the polynomials can be expressed using
cyclic hypertrees. We also propose a conjecture on the action of the symmetric
groups on the homology of these posets. On the other hand, we show that
Vallette's poset of pointed partitions is homotopy equivalent to Pitman's poset
of forests. The implicit common thema of the article is the combinatorics of
the PreLie operad.
