Combinatorial structure of group divisible designs without α-resolution classes in each group

Group Divisible Designs with Two Associate Classes and λ2=1

A pairwise balanced design is an ordered pair S,B , denoted PBD S,B , where S is a finite set of symbols, and B is a collection of subsets of S called blocks, such that each pair of distinct elements of S occurs together in exactly one block of B. Here |S| v is called the order of the PBD. Note that there is no condition on the size of the blocks in B. If all blocks are of the same size k, then...

Construction of Group Divisible Designs

Divisible designs with dual translation group

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space. AMS Classification: 05B05, 05B30, 20B25, 51N10

(3, Λ)-group Divisible Covering Designs

Let U, g, k and A be positive integers with u :::: k. A (k, A)-grOUp divisible covering design ((k, A)-GDCD) with type gU is a A-cover of pairs by k-tuples of a gu-set X with u holes of size g, which are disjoint and spanning. The covering number, C(k, A; gil), is the minimum number of blocks in a (k, A)-GDCD of type gUo In this paper, the detennination ofllie fimction C(3, A; gil) begun by [6]...

Resolvable Group Divisible Designs with Large Groups

We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete mult...