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 symmetric groups on the Whitney homology of these posets. In addition, we show that Vallette's poset of pointed partitions is homotopy equivalent to Pitman's poset of forests. The implicit common theme of these topics is the combinatorics of the PreLie operad.
Homology, Homotopy and Applications, Vol. 9 (2007), No. 1, pp.193-212.
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