Group divisible (K4−e)-packings with any minimum leave

Packings with large minimum kissing numbers

For each proper power of 4, n, we describe a simple explicit construction of a finite collection of pairwise disjoint open unit balls in R in which each ball touches more than 2 √ n others. A packing of balls in the Euclidean space is a finite or infinite collection of pairwise disjoint open unit balls in Rn. It is called a lattice packing if the centers of the balls form a lattice in Rn. The m...

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

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...

Construction of Group Divisible Designs

Class-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs

We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master de...