BGU Seminar on Algebraic Combinatorics Date: Tuesday, March 20, 2012 Time: 16:10 - 18:00 Place: The Deichmann Building for Mathematics, room -101 Speaker: Sven Reichard Essen, Germany; long term visitor at BGU Title: Enumeration of Strongly Regular Designs Abstract: Coherent configurations (CC's), in the sense of D.G. Higman, play a central role in Algebraic graph theory. They capture some of the combinatorial properties of permutation groups. However in contrast to other combinatorial structures no catalogue of such configurations of small order exists. Our long term goal is to fill this gap. We can classify coherent configurations according to the number of fibers (a combinatorial analogue of orbits of permutation groups). CC's with one fiber are actually association schemes, and for this type of structure a catalogue exists, see <http://kissme.shinshu-u.ac.jp/as/.> It is natural to consider CC's with two fibers next. One particular case of two-fiber CC's is equivalent to strongly regular designs (SRD's), a class of block designs introduced by Higman in 1988. While Higman originally was interested only in structures with primitive point and block graphs, we consider also the imprimitive case. We will describe our approach to construct all small SRD's and will consider a list of feasible parameter sets that we generated. Then we will give two examples: A classical object (Reye's configuration, discovered in 1882) in a new disguise, and a new object, namely the smallest non-Schurian SRD with 8 points and 12 blocks. If time allows, a few other small structures (Schurian and non-Schurian) will be briefly discussed. This is a joint project with Mikhail Klin. ******************************************************************** Dr. Mikhail Klin Department of Mathematics Ben-Gurion University of the Negev P.O.Box 653, Beer Sheva 84105, Israel Tel: (0)8/6477-811 (office) Fax: +972-(0)8/6477-648 e-mail: <klin@cs.bgu.ac.il> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Mikhail Klin <klin@cs.bgu.ac.il>