Bar-Ilan Combinatorics Seminar
 
The next meeting of the seminar will take place, IYH,
 
(when)  Sunday, 2 Nisan (March 25), 14:00-15:30
 
(where) Room 201 (Math & CS Seminar Room), Building 216, Bar-Ilan
University
 
(who)    Sven Reichard (Essen and Ben-Gurion University)
 
(what)   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.
 
This is a joint project with Mikhail Klin.
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You are all invited! Graduate students are especially welcome.
Seminar organizer: Ron Adin   <radin@math.biu.ac.il> 
Seminar's homepage:
  <http://www.math.biu.ac.il/~radin/comsem/comsem.html> 
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---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ron Adin   <radin@math.biu.ac.il>