Colloquium Announcement
Department of Mathematics
West Virginia University
for
Thursday, September 17,1998, at 3:45pm
in 315 Armstrong Hall
(Tea and cookies begin at 3:00 in coffee room.)
Professor Antony Hilton
Reading University and Eberly Professor at WVU
Symmetric Hamiltonian Double Latin Squares
The talk will be suitable for a general audience.
Students are strongly encouraged to participate.
Abstract
A double latin square is a 2n x 2n matrix on n sybbols
such that each symbol occurs exactly twice in each row and column.
The occurrences of a symbol \sigma describe a set of disjoint
cycles in a double latin square. Thus, for example, the cells of
such a cycle of length 2l might be:
(\rho_1,c_1),(\rho_1,c_2),(\rho_2,c_2),
(\rho_2,c_3),...,(\rho_l,c_l),(\rho_l,c_1),(\rho_1,c_1).
A cycle of length 4n is called a Hamiltonian cycle.
If the occurrences of each symbol describe a Hamiltonian cycle,
then the double latin square is called Hamiltonian.
An example of a symmetric Hamiltonian double latin square is:
1 3 3 2 1 2
3 2 1 1 3 2
3 1 3 2 2 1
2 1 2 1 3 3
1 3 2 3 2 1
2 2 1 3 1 3
We shall talk about various aspects of symmetric Hamiltonian
double latin squares.
The information on the future (and past) Colloquia can be also found on web at the
address:
http://www.math.wvu.edu/homepages/kcies/colloquium.html