  We consider bound states of strings which arise in 6d (1,0) SCFTs that are
realized in F-theory in terms of linear chains of spheres with negative
self-intersections 1,2, and 4. These include the strings associated to N small
E8 instantons, as well as the ones associated to M5 branes probing A and D type
singularities in M-theory or D5 branes probing ADE singularities in Type IIB
string theory. We find that these bound states of strings admit (0,4)
supersymmetric quiver descriptions and show how one can compute their elliptic
genera.
