Prof. dr. Ilya Ponomarenko: On quasi-thin association schemes

Date of publication: 12. 6. 2011
Mathematics colloquium
Četrtek, 16. 6. 2011, ob 16:15 v predavalnici 2.02 na Jadranski 21.
Ilya Ponomarenko
 
Petersburg Department of V. A. Steklov Institute of Mathematics, Rusija
 
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 result is that any non-Kleinian quasi-thin scheme is the two-orbit scheme of a suitable permutation group.
 
This is joint work with M. Muzychuk.