  Many-photon interference in linear-optics setups can be exploited to generate
and detect multipartite entanglement. Without recurring to any inter-particle
interaction, many entangled states have been created experimentally, and a
panoply of theoretical schemes for the generation of various classes of
entangled states is available. Here, we present a unifying framework that
accommodates the present experiments and theoretical protocols for the creation
of multiparticle entanglement via interference. A general representation of the
states that can be created is provided for bosons and fermions, for any
particle number, and for any dimensionality of the entangled degree of freedom.
Using the framework, we derive an upper bound on the generalized Schmidt number
of the states that can be generated, and we establish bounds on the
dimensionality of the manifold of these states. We show that - at the expense
of a smaller success probability - more states can be created with bosons than
with fermions, and give an intuitive interpretation of the state representation
and of the established bounds in terms of superimposed many-particle paths.
