  We construct a broad class of solutions of the KP-I equation by using a
reduced version of the Grammian form of the $\tau$-function. The basic solution
is a linear periodic chain of lumps propagating with distinct group and wave
velocities. More generally, our solutions are evolving linear arrangements of
lump chains, and can be viewed as the KP-I analogues of the family of
line-soliton solutions of KP-II. However, the linear arrangements that we
construct for KP-I are more general, and allow degenerate configurations such
as parallel or superimposed lump chains. We also construct solutions describing
interactions between lump chains and individual lumps, and discuss the
relationship between the solutions obtained using the reduced and regular
Grammian forms.
