  We describe and study a four parameters deformation of the two products and
the coproduct of the Hopf algebra of plane posets. We obtain a family of
braided Hopf algebras, generally self-dual. We also prove that in a particular
case (when the second parameter goes to zero and the first and third parameters
are equal), this deformation is isomorphic, as a self-dual braided Hopf
algebra, to a deformation of the Hopf algebra of free quasi-symmetric
functions.
