  A class of associative (super) algebras is presented, which naturally
generalize both the symmetric algebra $Sym(V)$ and the wedge algebra $\wedge
(V)$, where $V$ is a vector-space. These algebras are in a bijection with those
subsets of the set of the partitions which are closed under inclusions of
partitions. We study the rate of growth of these algebras, then characterize
the case where these algebras satisfy polynomial identities.
