  We construct maximal green sequences of maximal length for any affine quiver
of type $A$. We determine which sets of modules (equivalently $c$-vectors) can
occur in such sequences and, among these, which are given by a linear stability
condition (also called a central charge). There is always at least one such
maximal set which is linear. The proofs use representation theory and three
kinds of diagrams shown in Figure 1. Background material is reviewed with
details presented in two separate papers [arxiv:1706.06986] and
[arXiv:1706.06503].
