Mathematics Department Colloquium, CSU
March 21, 2008
4PM–5PM RT 1516
Classification of Orthogonal Arrays
by Integer Programming
Dursun Bulutoglu,
Air Force Institute of Technology
Abstract. Factorial designs are used extensively in a wide range
of scientific and industrial investigations for extracting as much information as possible at a fixed cost. Statisticians are interested
in finding orthogonal arrays, since orthogonal arrays are the most
efficient factorial designs for certain statistical models. However,
finding an orthogonal array that is universally optimal for a statistical model is a difficult unsolved problem. In fact, mathematicians
have worked on variants of this problem since the time of Euler.
Since statistical properties of orthogonal arrays are preserved under
design isomorphism, classifying them up to isomorphism allows the
best to be found with respect to the statistical property of choice. In
Bulutoglu and Margot (2007), the problem of classifying all isomorphism classes of OA(N, k, s, t)s is shown to be equivalent to finding
all isomorphism classes of non-negative integer solutions to a system of linear equations under the symmetry group of the equations.
This talk will introduce these ideas at a basic level; examples will
be provided.
* Refreshments at 3:30 PM in RT 1517