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>