February 3 Math Colloquium
Dinesh Sarvate, CofC
Group Divisible Designs : A new direction
A group divisible design GDD(n; m; k; λ1; λ2) is a collection of k-element subsets, called blocks, of an nm-set X where the elements of X are partitioned into m subsets (called groups) of size n each; pairs of distinct elements within the same group are called f rst associates of each other and appear together in λ1 blocks while any two elements not in the same group are called second associates and appear together in λ2 blocks. In the last few years there is a flurry of activity on the existence of Group Divisible Designs, but the general problem is still unfinished. These designs are an important part of Combinatorial Design Theory, not just because of their application but also because they provide a challenging area in the construction of combinatorial designs. We will demonstrate a construction of a GDD and then, keeping up with today's world, point out a challenging and new direction for GDDs to add more chaos in the already complicated situation.