Geodesic
Action of the symmetric groups on the homology of the hypertree posets
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 4, pp. 915-945.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The set of hypertrees on $n$ vertices can be endowed with a poset structure. J. McCammond and J. Meier computed the dimension of the unique non-zero homology group of the hypertree poset. We give another proof of their result and use the theory of species to determine the action of the symmetric group on this homology group, which is linked with the anti-cyclic structure of the PreLie operad. We also compute the action on the Whitney homology of the poset.
Classification : 05E18, 06A11
Keywords: hypertree, poset homology, Whitney homology, species, symmetric group action 
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     author = {Oger, B\'er\'enice},
     title = {Action of the symmetric groups on the homology of the hypertree posets},
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Oger, Bérénice. Action of the symmetric groups on the homology of the hypertree posets. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 4, pp. 915-945. http://geodesic.mathdoc.fr/item/JAC_2013__38_4_a3/