Title: On quasi-thin association schemes (joint with M.Muzychuk)

Abstract: An association scheme is called quasi-thin if the valency of each its basic relation is one or two. A quasi-thin scheme is Kleinian if its thin residue is the Klein four-group with respect to relational product.
It turns out that any Kleinian scheme arises from near-pencil on 3 points, or affine or projective plane of order 2. The main esult is that any non-Kleinian quasi-thin scheme is the two-orbit scheme of a suitable permutation group.