  Three families of posets depending on a nonnegative integer parameter $m$ are
introduced. The underlying sets of these posets are enumerated by the $m$-Fuss
Catalan numbers. Among these, one is a generalization of Stanley lattices and
another one is a generalization of Tamari lattices. The three families of
posets are related: they fit into a chain for the order extension relation and
they share some properties. Two associative algebras are constructed as
quotients of generalizations of the Malvenuto-Reutenauer algebra. Their
products describe intervals of our analogues of Stanley lattices and Tamari
lattices. In particular, one is a generalization of the Loday-Ronco algebra.
