Algebraic structures on double and plane posets

Loïc Foissy (1)

1 LMR - Laboratoire de Mathématiques de Reims

We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets "without N". We prove that they are free, cofree, self-dual, and we give an explicit Hopf pairing on these Hopf algebras. We also prove that they are free 2-As algebras; in particular, the Hopf algebra of posets "without N" is the free 2-As algebra on one generator. We deduce a description of the operads of 2-As algebras and of B_infty algebras in terms of plane posets.

Mots clés: Combinatorial Hopf algebras; 2-As algebras; Double posets; Plane posets.; Plane posets

Domaines: Anneaux et algèbres [math.RA]

Loïc Foissy. Algebraic structures on double and plane posets. Journal of Algebraic Combinatorics, 2013. ⟨hal-00559648v5⟩