The schurity problem for quasi-thin association schemes

Ilya Ponomarenko (Saint Petersburg Department of V. A. Steklov Institute of Mathematics, Saint Petersburg, Russian Federation)

An association scheme is called quasi-thin if the valency of each its basis relation is one or two. It is known that not each quasi-thin scheme is Schurian, i.e. one the basis relations of which are the 2-orbits of its automorphism group. Our main result gives a strong restriction for the structure of a non-schurian quasi-thin scheme.