Séminaire Lotharingien de Combinatoire, B72d (2015), 22 pp.

Bérénice Oger

Incidence Hopf Algebra of the Hypertree Posets

Abstract. We adapt the computation of characters on incidence Hopf algebras introduced by Schmitt in the 1990s for families of bounded posets to a family mixing bounded and unbounded finite posets. This computation relies on the introduction of an auxiliary bialgebra: the coproduct in this bialgebra enables us to compute the convolution of some characters on the incidence Hopf algebra. After establishing a general result on the link between the bialgebra and the incidence Hopf algebra, we apply it to the family of hypertree posets and partition posets. This link for hypertree posets enables us to recover the Möbius numbers of these posets due to the coproduct in the associated bialgebra. This coproduct is computed using the number of hypertrees with fixed valency set and fixed edge sizes set.

Received: March 18, 2014. Accepted: May 25, 2015.

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