Hypertree posets and hooked partitions

Bérénice Oger (1)

1 AGL - Algèbre, géométrie, logique

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.

Mots clés: Poset; Incidence Hopf algebra; Hypertree; Moebius number

Domaines: Combinatoire [math.CO]; Anneaux et algèbres [math.RA]

Bérénice Oger. Hypertree posets and hooked partitions. 2014. ⟨hal-00957978⟩