Algebraic structures on double and plane posets
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 ? algebras in terms of plane posets.
plane posets double posets 2-as algebras combinatorial hopf algebras