  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.
