SEMINAR AT QMUL
Joint meeting of Combinatorics and Design Study Groups
D.A.Preece and N.C.K.Phillips
"Balanced Graeco-Latin designs equivalent to triple arrays:
a major break-through"
ALL ARE WELCOME
Wednesday 3rd July 2002, 11.30 a.m.
Mathematics Seminar Room, School of Mathematical Sciences,
Queen Mary, University of London
Mile End Road, London E1 4NS
Abstract
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Years ago, Preece posed the following problem:
Take a solution of the Kirkman School-girls problem,
or indeed any balanced incomplete block design with
v = 15 , k = 3 , b = 35 , r = 7 .
Take also a balanced incomplete block design (BIBD) with
v = 7 , k = 3 , b = 35 , r = 15 .
Can these be superimposed into a Graeco-Latin design
(with b = 35 , k = 3 ) such that
(a) each treatment from the first BIBD [say, each girl] occurs
exactly once with each treatment from the second BIBD [say,
each colour], and
(b) the design is balanced overall?
Phillips is part of the team at Southern Illinois University that
have obtained superimpositions having the required properties.
These superimpositions, written as 7 x 15 arrays (with 7 rows
for the 7 colours, 15 columns for the 15 girls, and entries
1,2,...,35 denoting the block numbers), are special cases of what
the team calls "triple arrays".
Preece will describe the class of Graeco-Latin designs that are
equivalent to triple arrays, will explain the equivalence, and
will discuss issues that arise when considering whether two
designs having the same parameters are isomorphic.
Phillips will describe how the successful computer search for
designs was implemented and will indicate the great speed with
which the computer program produces designs.
A detailed study has yet to be made of the non-isomorphic designs
that can be produced.
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